
<PAGE>

                                                                     EXHIBIT 3.1
 
                           KILROY REALTY CORPORATION

                            ARTICLES SUPPLEMENTARY

                                700,000 SHARES

             9 3/8% SERIES C CUMULATIVE REDEEMABLE PREFERRED STOCK


          Kilroy Realty Corporation, a Maryland corporation (the "Company"),
                                                                  -------   
hereby certifies to the State Department of Assessments and Taxation of Maryland
that:

          FIRST:    Pursuant to the authority expressly vested in the Board of
          -----                                                               
Directors of the Company by Article IV of the Articles of Amendment and
Restatement of the Company filed with the Department on January 21, 1997, which
comprises, together with the Articles Supplementary (the "Series A Articles
                                                          -----------------
Supplementary") filed by the Corporation on February 6, 1998 and April 20, 1998
-------------                                                                  
establishing a class of preferred stock of the Corporation, par value $0.01 per
share (the "Preferred Stock"), designated as the "8.073% Series A Cumulative
            ---------------                                                 
Redeemable Preferred Stock" (the "Series A Preferred Stock"), the Articles
                                  ------------------------                
Supplementary (the "Series B Articles Supplementary") filed by the Corporation
                    -------------------------------                           
on October 15, 1998, establishing a class of Preferred Stock designated as the
Series B Junior Participating Preferred Stock (the "Series B Preferred Stock")
                                                    ------------------------  
and these Articles Supplementary, the charter (the "Charter") and Section 2-105
                                                    -------                    
of the Maryland General Corporation Law (the "MGCL"), the Board of Directors of
                                              ----                             
the Company (the "Board of Directors"), by resolution duly adopted on November
                  ------------------                                          
19, 1998 has classified 700,000 shares of the authorized but unissued Preferred
Stock as a separate class of Preferred Stock, authorized the issuance of a
maximum of 700,000 shares of such class of Preferred Stock, set certain of the
preferences, conversion and other rights, voting powers, restrictions,
limitations as to dividends, qualifications, terms and conditions of redemption
and other terms and conditions of such class of Preferred Stock, and pursuant to
the powers contained in the Bylaws of the Company and the MGCL, appointed a
committee (the "Committee") of the Board of Directors and delegated to the
                ---------                                                 
Committee, to the fullest extent permitted by the MGCL and the Charter and
Bylaws of the Company, all powers of the Board of Directors with respect to
designating, and setting all other preferences, conversion and other rights,
voting powers, restrictions, limitations as to dividends and other
distributions, qualifications and terms and conditions of redemption of, such
class of Preferred Stock determining the number of shares of such class of
Preferred Stock (not in excess of the aforesaid maximum number) to be issued and
the consideration and other terms and conditions upon which such shares of such
class of Preferred Stock are to be issued.

          SECOND:   Pursuant to the authority conferred upon the Committee as
          ------                                                             
aforesaid, the Committee has unanimously adopted resolutions designating the
aforesaid class of Preferred Stock as the "9 3/8% Series C Cumulative Redeemable
Preferred Stock," setting the preferences, conversion and other rights, voting
powers, restrictions, limitations as to dividends, qualifications, terms and
conditions of redemption and other terms and conditions of such 9 3/8% Series C
Cumulative Redeemable Preferred Stock (to the extent not set by the Board of
Directors in the

[SEAL]
                               STATE OF MARYLAND
                               -----------------

I hereby certify that this is a true and complete copy of the       23
                                                              -------------
page document on file in this office DATED:       11/25/98
                                            ---------------------
             STATE DEPARTMENT OF ASSESSMENTS AND TAXATION
BY:              Darla D. Simms                               , Custodian
   -----------------------------------------------------------
This stamp replaces our previous certification system.  Effective: 6/95
<PAGE>
 
resolutions referred to in Article FIRST of these Articles Supplementary) and
                                   -----
authorizing the issuance of up to 700,000 shares of 9 3/8% Series C Cumulative
Redeemable Preferred Stock.

          THIRD:      The class of Preferred Stock of the Company created by the
          -----                                                               
resolutions duly adopted by the Board of Directors of the Company and by the
Committee and referred to in Articles FIRST and SECOND of these Articles
                                      -----     ------                  
Supplementary shall have the following designation, number of shares,
preferences, conversion and other rights, voting powers, restrictions and
limitations as to dividends, qualifications, terms and conditions of redemption
and other terms and conditions:

          Section 1.  Designation and Number.  A series of Preferred Stock,
                      ----------------------                               
designated the "9 3/8% Series C Cumulative Redeemable Preferred Stock" (the
"Series C Preferred Stock") is hereby established.  The number of shares of
Series C Preferred Stock shall be 700,000.

          Section 2.  Rank.  The Series C Preferred Stock will, with respect
                      ----                                                  
to distributions and rights upon voluntary or involuntary liquidation, winding-
up or dissolution of the Company, rank senior to all classes or series of Common
Stock (as defined in the Charter), the Series B Preferred Stock, and to all
classes or series of equity securities of the Company now or hereafter
authorized, issued or outstanding, other than the Series A Preferred Stock and
any class or series of equity securities of the Company expressly designated as
ranking on a parity with or senior to the Series C Preferred Stock as to
distributions or rights upon voluntary or involuntary liquidation, winding-up or
dissolution of the Company, or both.  For purposes of these Articles
Supplementary, the term "Parity Preferred Stock" shall be used to refer to the
                         ----------------------                               
Series A Preferred Stock and any class or series of equity securities of the
Company now or hereafter authorized, issued or outstanding expressly designated
by the Company to rank on a parity with Series C Preferred Stock with respect to
distributions or rights upon voluntary or involuntary liquidation, winding-up or
dissolution of the Company, or both, as the context may require.  The term
"equity securities" does not include debt securities, which will rank senior to
the Series C Preferred Stock prior to conversion.

          Section 3.  Distributions.
                      ------------- 

          (a) Payment of Distributions.  Subject to the rights of holders of
              ------------------------                                      
Parity Preferred Stock as to the payment of distributions and holders of equity
securities ranking senior to the Series C Preferred Stock as to payment of
distributions, holders of Series C Preferred Stock will be entitled to receive,
when, as and if declared by the Company, out of funds legally available for the
payment of distributions, cumulative preferential cash distributions at the rate
per annum of 9 3/8% of the $50.00 liquidation preference per share of Series C
Preferred Stock.  Such distributions shall be cumulative, shall accrue from the
original date of issuance and will be payable quarterly (such quarterly periods
for purposes of payment and accrual will be the quarterly periods ending on the
dates specified in this sentence and not calendar year quarters) in arrears, on
the 15th of February, May, August and November of each year and, in the event of
a redemption, on the redemption date (each a "Preferred Stock Distribution
                                              ----------------------------
Payment Date"), commencing in each case on the first Preferred Stock
------------                                                        
Distribution Payment Date after the original date of issuance.  The amount of
the distribution payable for any period will be computed on the basis of a 360-
day year of twelve 30-day

                                       2
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months and for any period shorter than a full quarterly period for which
distributions are computed, the amount of the distributions payable will be
computed on the basis of the actual number of days elapsed in such a 30-day
month. If any date on which distributions are to be made on the Series C
Preferred Stock is not a Business Day (as defined herein), then payment of the
distribution to be made on such date will be made on the next succeeding day
that is a Business Day (and without any interest or other payment in respect of
any such delay) except that, if such Business Day is in the next succeeding
calendar year, such payment shall be made on the immediately preceding Business
Day, in each case with the same force and effect as if made on such date.
Distributions on the Series C Preferred Stock will be made to the holders of
record of the Series C Preferred Stock on the relevant record dates, which,
unless otherwise provided by the Company with respect to any distribution, will
be 15 Business Days prior to the relevant Preferred Stock Distribution Payment
Date (each a "Distribution Record Date"). Notwithstanding any provision to the
              ------------------------
contrary contained herein, each outstanding share of Series C Preferred Stock
shall be entitled to receive, and shall receive, a dividend with respect to any
Distribution Record Date equal to the dividend paid with respect to each other
share of Series C Preferred Stock which is outstanding on such date. In
addition, notwithstanding anything to the contrary set forth herein, each share
of Series C Preferred Stock shall also continue to accrue all accrued and unpaid
distributions up to the exchange date on any Series C Preference Unit (as
defined in the Fourth Amended and Restated Limited Partnership Agreement of
Kilroy Realty, L.P. dated as of November 24, 1998 (the "Partnership Agreement"))
                                                        ---------------------
validly exchanged into such share of Series C Preferred Stock in accordance with
the provisions of the Partnership Agreement .

          The term "Business Day" shall mean each day, other than a Saturday or
                    ------------                                               
a Sunday, which is not a day on which banking institutions in New York, New York
or Los Angeles, California are authorized or required by law, regulation or
executive order to close.

          (b) Limitation on Distributions.  No distributions on the Series C
              ---------------------------                                   
Preferred Stock shall be declared or paid or set apart for payment by the
Company at such time as the terms and provisions of any agreement of the
Company, including any agreement relating to its indebtedness, prohibits such
declaration, payment or setting apart for payment or provides that such
declaration, payment or setting apart for payment would constitute a breach
thereof or a default thereunder, or if such declaration, payment or setting
apart for payment shall be restricted or prohibited by law.

          (c) Distributions Cumulative.  Notwithstanding the foregoing,
              ------------------------                                 
distributions on the Series C Preferred Stock will accrue whether or not the
terms and provisions set forth in Section 3(b) hereof at any time prohibit the
current payment of distributions, whether or not the Company has earnings,
whether or not there are funds legally available for the payment of such
distributions and whether or not such distributions are authorized.  Accrued but
unpaid distributions on the Series C Preferred Stock will accumulate as of the
Preferred Stock Distribution Payment Date on which they first become payable.
Accumulated and unpaid distributions will not bear interest.

          (d) Priority as to Distributions.
              ---------------------------- 

                                       3
<PAGE>
 
              (i)     So long as any Series C Preferred Stock is outstanding, no
distribution of cash or other property shall be authorized, declared, paid or
set apart for payment on or with respect to any class or series of Common Stock
or any class or series of other stock of the Company ranking junior as to the
payment of distributions to the Series A Preferred Stock and the Series C
Preferred Stock (such Common Stock or other junior stock, including, without
limitation, the Series B Preferred Stock, collectively, "Junior Stock"), nor
                                                         ------------       
shall any cash or other property be set aside for or applied to the purchase,
redemption or other acquisition for consideration of any Series C Preferred
Stock, any Parity Preferred Stock with respect to distributions or any Junior
Stock, unless, in each case, all distributions accumulated on all Series C
Preferred Stock and all classes and series of outstanding Parity Preferred Stock
as to payment of distributions have been paid in full.  The foregoing sentence
will not prohibit (i) distributions payable solely in Junior Stock, (ii) the
conversion of Junior Stock or Parity Preferred Stock into stock of the company
ranking junior to the Series C Preferred Stock as to distributions, and (iii)
purchase by the Company of such Series C Preferred Stock, Parity Preferred Stock
with respect to distributions or Junior Stock pursuant to Section 7 of this
Article Third and comparable Charter provisions with respect to other classes of
capital stock of the Company to the extent required to preserve the Company's
status as a real estate investment trust.

          (ii)        So long as distributions have not been paid in full (or a
sum sufficient for such full payment is not so set apart) upon the Series C
Preferred Stock, all distributions authorized and declared on the Series C
Preferred Stock and all classes or series of outstanding Parity Preferred Stock
(including Series A Preferred Stock) with respect to distributions shall be
authorized and declared so that the amount of distributions authorized and
declared per share of Series C Preferred Stock and such other classes or series
of Parity Preferred Stock (including Series A Preferred Stock) shall in all
cases bear to each other the same ratio that accrued distributions per share on
the Series C Preferred Stock and such other classes or series of Parity
Preferred Stock (including Series A Preferred Stock) (which shall not include
any accumulation in respect of unpaid distributions for prior distribution
periods if such class or series of Parity Preferred Stock do not have cumulative
distribution rights) bear to each other.

          (e) No Further Rights.  Holders of Series C Preferred Stock shall not
              -----------------                                                
be entitled to any distributions, whether payable in cash, other property or
otherwise, in excess of the full cumulative distributions described herein.

          (f) Capital Gain Dividend.  If, for any taxable year, the Company
              ---------------------                                        
elects to designate as a "capital gain dividend" (as defined in Section 857 of
the Internal Revenue Code of 1986, as amended), any portion (the "Capital Gains
Amount") of the dividends paid or made available for the year to holders of any
class or series of stock of the Company, the portion of the Capital Gains Amount
that shall be allocable to holders of the Series C Preferred Stock shall be the
amount that the total dividends (as determined for federal income tax purposes)
paid or made available to the holders of the Series C Preferred Stock for the
year bears to the aggregate amount of dividends (as determined for federal
income tax purposes) paid or made available to the holders of all classes or
series of stock of the Company for such year.

                                       4
<PAGE>
 
          Section 4.  Liquidation Preference.
                      ---------------------- 

          (a) Payment of Liquidating Distributions.  Subject to the rights of
              ------------------------------------                           
holders of Parity Preferred Stock with respect to rights upon any voluntary or
involuntary liquidation, dissolution or winding-up of the Company and subject to
equity securities ranking senior to the Series C Preferred Stock with respect to
rights upon any voluntary or involuntary liquidation, dissolution or winding-up
of the Company, the holders of Series C Preferred Stock shall be entitled to
receive out of the assets of the Company legally available for distribution or
the proceeds thereof, after payment or provision for debts and other liabilities
of the Company, but before any payment or distributions of the assets shall be
made to holders of Common Stock or any other class or series of shares of the
Company that ranks junior to the Series C Preferred stock as to rights upon
liquidation, dissolution or winding-up of the Company, an amount equal to the
sum of (i) a liquidation preference of $50 per share of Series C Preferred
Stock, and (ii) an amount equal to any accumulated and unpaid distributions
thereon to the date of payment.  In the event that, upon such voluntary or
involuntary liquidation, dissolution or winding-up, there are insufficient
assets to permit full payment of liquidating distributions to the holders of
Series C Preferred Stock and any Parity Preferred Stock as to rights upon
liquidation, dissolution or winding-up of the Company, all payments of
liquidating distributions on the Series C Preferred Stock and such Parity
Preferred Stock shall be made so that the payments on the Series C Preferred
Stock and such Parity Preferred Stock shall in all cases bear to each other the
same ratio that the respective rights of the Series C Preferred Stock and such
other Parity Preferred Stock (which shall not include any accumulation in
respect of unpaid distributions for prior distribution periods if such Parity
Preferred Stock do not have cumulative distribution rights) upon liquidation,
dissolution or winding-up of the Company bear to each other.

          (b) Notice.  Written notice of any such voluntary or involuntary
              ------                                                      
liquidation, dissolution or winding-up of the Company, stating the payment date
or dates when, and the place or places where, the amounts distributable in such
circumstances shall be payable, shall be given by (i) fax and (ii) by first
class mail, postage pre-paid, not less than 30 and not more that 60 days prior
to the payment date stated therein, to each record holder of the Series C
Preferred Stock at the respective addresses of such holders as the same shall
appear on the share transfer records of the Company.

          (c) No Further Rights.  After payment of the full amount of the
              -----------------                                          
liquidating distributions to which they are entitled, the holders of Series C
Preferred Stock will have no right or claim to any of the remaining assets of
the Company.

          (d) Consolidation, Merger or Certain Other Transactions.  The
              ---------------------------------------------------      
consolidation or merger or other business combination of the Company with or
into any corporation, trust or other entity (or of any corporation, trust or
other entity with or into the Company) shall not be deemed to constitute a
liquidation, dissolution or winding-up of the Company.

          (e) Permissible Distributions.  In determining whether a distribution
              -------------------------                                        
(other than upon voluntary or involuntary liquidation) by dividend, redemption
or other acquisition of shares

                                       5
<PAGE>
 
of stock of the Company or otherwise is permitted under the MGCL, no effect
shall be given to amounts that would be needed, if the Company were to be
dissolved at the time of the distribution, to satisfy the preferential rights
upon dissolution of holders of shares of stock of the Company whose preferential
rights upon dissolution are superior to those receiving the distribution.

          Section 5.  Optional Redemption.
                      ------------------- 

          (a) Right of Optional Redemption.  The Series C Preferred Stock may
              ----------------------------                                   
not, subject to Section 7 hereof, be redeemed prior to November 24, 2003.  On or
after such date, the Company shall have the right to redeem the Series C
Preferred Stock, in whole or in part, at any time or from time to time, upon not
less than 30 nor more than 60 days' written notice, at a redemption price,
payable in cash, equal to $50 per share of Series C Preferred Stock plus
accumulated and unpaid distributions to the date of redemption.  If fewer than
all of the outstanding shares of Series C Preferred Stock are to be redeemed,
the shares of Series C Preferred Stock to be redeemed shall be selected pro rata
(as nearly as practicable without creating fractional units).

          (b) Limitation on Redemption.
              ------------------------ 

              (i)     The redemption price of the Series C Preferred Stock
(other than the portion thereof consisting of accumulated but unpaid
distributions) will be payable solely out of the sale proceeds of capital stock
of the Company and from no other source. For purposes of the preceding sentence,
"capital stock" means any equity securities (including Common Stock and
Preferred Stock), shares, participation or other ownership interests (however
designated) and any rights (other than debt securities convertible into or
exchangeable for equity securities) or options to purchase any of the foregoing.

              (ii)    Subject to Section 7 hereof, the Company may not redeem
fewer than all of the outstanding shares of Series C Preferred Stock unless all
accumulated and unpaid distributions have been paid on all Series C Preferred
Stock for all quarterly distribution periods terminating on or prior to the date
of redemption.

          (c) Procedures for Redemption.
              ------------------------- 

              (i)     Notice of redemption will be (i) faxed, and (ii) mailed by
the Company, postage prepaid, not less than 30 nor more than 60 days prior to
the redemption date, addressed to the respective holders of record of the Series
C Preferred Stock to be redeemed at their respective addresses as they appear on
the transfer records of the Company. No failure to give or defect in such notice
shall affect the validity of the proceedings for the redemption of any Series C
Preferred Stock except as to the holder to whom such notice was defective or not
given. In addition to any information required by law or by the applicable rules
of any exchange upon which the Series C Preferred Stock may be listed or
admitted to trading, each such notice shall state: (i) the redemption date, (ii)
the redemption price, (iii) the number of shares of Series C Preferred Stock to
be redeemed, (iv) the place or places where such shares of Series C Preferred
Stock are to be surrendered for payment of the redemption price, (v) that
distributions on the Series C Preferred

                                       6
<PAGE>
 
Stock to be redeemed will cease to accumulate on such redemption date and (vi)
that payment of the redemption price and any accumulated and unpaid
distributions will be made upon presentation and surrender of such Series C
Preferred Stock. If fewer than all of the shares of Series C Preferred stock
held by any holder are to be redeemed, the notice mailed to such holder shall
also specify the number of shares of Series C Preferred Stock held by such
holder to be redeemed.

              (ii)    If the Company gives a notice of redemption in respect of
Series C Preferred Stock (which notice will be irrevocable) then, by 12:00 noon,
New York City time, on the redemption date, the Company will deposit irrevocably
in trust for the benefit of the Series C Preferred Stock being redeemed funds
sufficient to pay the applicable redemption price, plus any accumulated and
unpaid distributions, if any, on such shares to the date fixed for redemption,
without interest, and will give irrevocable instructions and authority to pay
such redemption price and any accumulated and unpaid distributions, if any, on
such shares to the holders of the Series C Preferred Stock upon surrender of the
Series C Preferred Stock by such holders at the place designated in the notice
of redemption.  On and after the date of redemption, distributions will cease to
accumulate on the Series C Preferred Stock or portions thereof called for
redemption, unless the Company defaults in the payment thereof.  If any date
fixed for redemption of Series C Preferred Stock is not a Business Day, then
payment of the redemption price payable on such date will be made on the next
succeeding day that is a Business Day (and without any interest or other payment
in respect of any such delay) except that, if such Business Day falls in the
next calendar year, such payment will be made on the immediately preceding
Business Day, in each case with the same force and effect as if made on such
date fixed for redemption.  If payment of the redemption price or any
accumulated or unpaid distributions in respect of the Series C Preferred Stock
is improperly withheld or refused and not paid by the Company, distributions on
such Series C Preferred Stock will continue to accumulate from the original
redemption date to the date of payment, in which case the actual payment date
will be considered the date fixed for redemption for purposes of calculating the
applicable redemption price and any accumulated and unpaid distributions.

          (d) Status of Redeemed Stock.  Any Series C Preferred Stock that shall
              ------------------------                                          
at any time have been redeemed shall after such redemption, have the status of
authorized but unissued Preferred Stock, without designation as to class or
series until such shares are once more designated as part of a particular class
or series by the Board of Directors.

          Section 6.  Voting Rights.
                      ------------- 

          (a) General.  Holders of the Series C Preferred Stock will not have
              -------                                                        
any voting rights, except as set forth below.

          (b) Right of Elect Directors.  (i) If at any time full distributions
              ------------------------                                        
shall not have been timely made on any Series C Preferred Stock with respect to
any six (6) prior quarterly distribution periods, whether or not consecutive, (a
"Preferred Distribution Default"), the holders such Series C Preferred Stock,
 ------------------------------                                              
voting together as a single class with the holders of each class or series of
Parity Preferred Stock upon which like voting rights have been conferred and are
exercisable, including the Series A Preferred Stock, will have the right to
elect two additional

                                       7
<PAGE>
 
directors to serve on the Company's Board of Directors (the "Preferred Stock
                                                             ---------------
Directors") at a special meeting called in accordance with Section 6(b)(ii)
---------
below or at the next annual meeting of stockholders, and at each subsequent
annual meeting of stockholders or special meeting held in place thereof, until
all such distributions in arrears and distributions for the current quarterly
period on the Series C Preferred Stock and each such class or series of Parity
Preferred Stock, including the Series A Preferred Stock, have been paid in full.
A distribution in respect of Series C Preferred Stock shall be considered timely
made if made within two (2) Business Days after the applicable Preferred Stock
Distribution Payment Date if at time of such late payment there shall not be any
prior quarterly distribution periods in respect of which full distributions were
not timely made at the applicable Preferred Stock Distribution Date.

              (ii)    At any time when such voting rights shall have vested, a
proper officer of the Company shall call or cause to be called, upon written
request of holders of record of at least 10% of the outstanding Shares of Series
C Preferred Stock, a special meeting of the holders of Series C Preferred Stock
and all the series of Parity Preferred Stock upon which like voting rights have
been conferred and are exercisable (collectively, the "Parity Securities") by
mailing or causing to be mailed to such holders a notice of such special meeting
to be held not less than ten and not more than 45 days after the date such
notice is given.  The record date for determining holders of the Parity
Securities entitled to notice of and to vote at such special meeting will be the
close of business on the third Business Day preceding the day on which such
notice is mailed.  At any such special meeting, all of the holders of the Parity
Securities, by plurality vote, voting together as a single class without regard
to series will be entitled to elect two directors on the basis of one vote per
$50.00 of liquidation preference to which such Parity Securities are entitled by
their terms (excluding amounts in respect of accumulated and unpaid dividends)
and not cumulatively.  The holder or holders of one-third of the Parity
Securities then outstanding, present in person or by proxy, will consitute a
quorum for the election of the Preferred Stock Directors except as otherwise
provided by law.  Notice of all meetings at which holders of the Series C
Preferred Shares shall be entitled to vote will be given to such holders at
their addresses as they appear in the transfer records.  At any such meeting or
adjournment thereof in the absence of a quorum, subject to the provisions of any
applicable law, a majority of the holders of the Parity Securities present in
person or by proxy shall have the power to adjourn the meeting for the election
of the Preferred Stock Directors, without notice other than an announcement at
the meeting, until a quorum is present.  If a Preferred Distribution Default
shall terminate after the notice of a special meeting has been given but before
such special meeting has been held, the Company shall, as soon as practicable
after such termination, mail or cause to be mailed notice of such termination to
holders of the Series C Preferred Shares that would have been entitled to vote
at such special meeting.

              (iii)   If and when all accumulated distributions and the
distribution for the current distribution period on the Series C Preferred Stock
shall have been paid in full or set aside for payment in full, the holders of
the Series C Preferred Stock shall be divested of the voting rights set forth in
Section 6(b) herein (subject to revesting in the event of each and every
Preferred Distribution Default) and, if all distributions in arrears and the
distributions for the current distribution period have been paid in full or set
aside for payment in full on all other classes or series of Parity Preferred
Stock upon which like voting rights have been conferred and are exercisable, the

                                       8
<PAGE>
 
term and office of each Preferred Stock Director so elected shall terminate.
Any Preferred Stock Director may be removed at any time with or without cause by
the vote of, and shall not be removed otherwise than by the vote of, the holders
of record of a majority of the outstanding Series C Preferred Stock when they
have the voting rights set forth in Section 6(b) (voting separately as a single
class with all other classes or series of Parity Preferred Stock, including the
Series A Preferred Stock, upon which like voting rights have been conferred and
are exercisable).  So long as a Preferred Distribution Default shall continue,
any vacancy in the office of a Preferred Stock Director may be filled by written
consent of the Preferred Stock Director remaining in office, or if none remains
in office, by a vote of the holders of record of a majority of the outstanding
Series C Preferred Stock when they have the voting rights set forth in Section
6(b) (voting separately as a single class with all other classes or series of
Parity Preferred Stock, including the Series A Preferred Stock, upon which like
voting rights have been conferred and are exercisable).  The Preferred Stock
Director shall each be entitled to one vote per director on any manner.

          (c) Certain Voting Rights.  So long as any Series C Preferred Stock
              ---------------------                                          
remains outstanding, the Company shall not, without the affirmative vote of the
holders of at least two-thirds of the Series C Preferred Stock outstanding at
the time (i) designate or create, or increase the authorized or issued amount
of, any class or series of shares ranking prior to the Series C Preferred Stock
with respect to payment of distributions or rights upon liquidation, dissolution
or winding-up or reclassify any authorized shares of the Company into any such
shares, or create, authorize or issue any obligations or security convertible
into or evidencing the right to purchase any such shares, (ii) designate or
create, or increase the authorized or issued amount of, any Parity Preferred
Stock or reclassify any authorized shares of the Company into any such shares,
or create, authorize or issue any obligations or security convertible into or
evidencing the right to purchase any such shares, but only to the extent such
Parity Preferred Stock is issued to an affiliate of the Company, or (iii) either
(A) consolidate, merge into or with, or convey, transfer or lease its assets
substantially as an entirety, to any corporation or other entity, or (B) amend,
alter or repeal the provisions of the Company's Charter (including these
Articles Supplementary) or Bylaws, whether by merger, consolidation or
otherwise, in each case that would materially and adversely affect the powers,
special rights, preferences, privileges or voting power of the Series C
Preferred Stock or the holders thereof; provided, however, that with respect to
the occurrence of any event set forth in (iii) above, so long as (a) the Company
is the surviving entity and the Series C Preferred stock remains outstanding
with the terms thereof unchanged, or (b) the resulting, surviving or transferee
entity is a corporation, business trust or other like entity organized under the
laws of any state and substitutes for the Series C Preferred Stock other
preferred stock having substantially the same terms and same rights as the
Series C Preferred Stock, including with respect to distributions, voting rights
and rights upon liquidation, dissolution or winding-up, then the occurrence of
any such event shall not be deemed to materially and adversely affect such
rights, privileges or voting powers of the holders of the Series C Preferred
Stock and provided further that any increase in the amount of authorized
Preferred Stock or the creation or issuance of any other class or series of
Preferred Stock, or any increase in an amount of authorized shares of each class
or series, in each case ranking either (a) junior to the Series C Preferred
Stock with respect to payment of distributions or the distribution of assets
upon liquidation, dissolution or winding-up, or (b) on a parity with the Series
C Preferred Stock with respect to payment of distributions or the distribution
of assets upon liquidation, dissolution or

                                       9
<PAGE>
 
winding-up to the extent such Preferred Stock is not issued to an affiliate of
the Company, shall not be deemed to materially and adversely affect such rights,
preferences, privileges or voting powers.

          Section 7.  Restrictions on Ownership and Transfer to Preserve Tax
                      ------------------------------------------------------
Benefit.
------- 

          (a) Definitions.  For the purposes of Section 7 of these Articles
              -----------                                                  
Supplementary, the following terms shall have the following meanings:

              "Beneficial Ownership" shall mean ownership of Series C Preferred
               --------------------                                            
          Stock by a Person who is or would be treated as an owner of such
          Series C Preferred Stock either actually or constructively through the
          application of Section 544 of the Code, as modified by Section
          856(h)(1)(B) of the Code.  The terms "Beneficial Owner," "Beneficially
          Owns" and "Beneficially Owned" shall have the correlative meanings.

              "Beneficial Ownership Limit" shall mean 7.0% (by value) of the
               --------------------------                                   
          outstanding shares of capital stock of the Company.

              "Charitable Beneficiary" shall mean one or more beneficiaries of
               ----------------------                                         
          a Trust, as determined pursuant to Section 7(c)(vi) of these Articles
          Supplementary, each of which shall be an organization described in
          Sections 170(b)(1)(A), 170(c)(2) and 501(c)(3) of the Code.

              "Code" shall mean the Internal Revenue Code of 1986, as amended.
               ----                                                            
          All section references to the Code shall include any successor
          provisions thereof as may be adopted from time to time.

              "Constructive Ownership" shall mean ownership of Series C
               ----------------------                                  
          Preferred Stock by a Person who is or would be treated as an owner of
          such Series C Preferred Stock either actually or constructively
          through the application of Section 318 of the Code, as modified by
          Section 856(d)(5) of the Code.  The terms "Constructive Owner,"
          "Constructively Owns" and "Constructively Owned" shall have the
          correlative meanings.

              "Constructive Ownership Limit" shall mean 9.8% (by value) of the
               ----------------------------                                   
          outstanding shares of capital stock the Company.

              "IRS" means the United States Internal Revenue Service.
               ---                                                   

              "Market Price" shall mean the last reported sales price reported
               ------------                                                   
          on the New York Stock Exchange of the Series C Preferred Stock on the
          trading day immediately preceding the relevant date, or if the Series
          C Preferred Stock is not then traded on the New York Stock Exchange,
          the last reported sales price of the Series C Preferred Stock on the
          trading day immediately preceding the relevant date as reported on any
          exchange or quotation system over which the Series C Preferred Stock
          may be

                                       10
<PAGE>
 
          traded, or if the Series C Preferred Stock is not then traded
          over any exchange or quotation system, the market price of the Series
          C Preferred Stock on the relevant date as determined in good faith by
          the Board of Directors of the Company.

              "MGCL" shall mean the Maryland General Corporation Law, as
               ----                                                     
          amended from time to time, and any successor statute hereafter
          enacted.

              "Operating Partnership" shall mean Kilroy Realty, L.P., a
               ---------------------                                   
          Delaware limited partnership.

              "Partnership Agreement" shall mean the Agreement of Limited
               ---------------------                                     
          Partnership of the Operating Partnership, as such agreement may be
          amended from time to time.

              "Person" shall mean an individual, corporation, partnership,
               ------                                                     
          limited liability company, estate, trust (including a trust qualified
          under Section 401(a) or 501(c)(17) of the Code), a portion of a trust
          permanently set aside for or to be used exclusively for the purposes
          described in Section 642(c) of the Code, association, private
          foundation within the meaning of Section 509(a) of the Code, joint
          stock company or other entity; but does not include an underwriter
          acting in a capacity as such in a public offering of shares of Series
          C Preferred Stock provided that the ownership of such shares of Series
          C Preferred Stock by such underwriter would not result in the Company
          being "closely held" within the meaning of Section 856(h) of the Code,
          or otherwise result in the Company failing to qualify as a REIT.

              "Purported Beneficial Transferee" shall mean, with respect to any
               -------------------------------                                 
          purported Transfer (or other event) which results in a transfer to a
          Trust, as provided in Section 7(b)(ii) of these Articles
          Supplementary, the Purported Record Transferee, unless the Purported
          Record Transferee would have acquired or owned shares of Series C
          Preferred Stock for another Person who is the beneficial transferee or
          owner of such shares, in which case the Purported Beneficial
          Transferee shall be such Person.

              "Purported Record Transferee" shall mean, with respect to any
               ---------------------------                                 
          purported Transfer (or other event) which results in a transfer to a
          Trust, as provided in Section 7(b)(ii) of these Articles
          Supplementary, the record holder of the Series C Preferred Stock if
          such Transfer had been valid under Section 7(b)(i) of these Articles
          Supplementary.

              "REIT" shall mean a real estate investment trust under Sections
               ----                                                          
          856 through 860 of the Code and, for purposes of taxation of the
          Company under applicable state law, comparable provisions of the law
          of such state.

                                       11
<PAGE>
 
              "Restriction Termination Date" shall mean the first day after the
               ----------------------------                                    
          date hereof on which the Board of Directors of the Company determines
          that it is no longer in the best interests of the Company to attempt
          to, or continue to, qualify as a REIT.

              "Transfer" shall mean any sale, transfer, gift, assignment,
               --------                                                  
          devise or other disposition of Series C Preferred Stock, (including
          (i) the granting of any option or entering into any agreement for the
          sale, transfer or other disposition of Series C Preferred Stock or
          (ii) the sale, transfer, assignment or other disposition of any
          securities (or rights convertible into or exchangeable for Series C
          Preferred Stock)), whether voluntary or involuntary, whether such
          transfer has occurred of record or beneficially or Beneficially or
          Constructively (including but not limited to transfers of interests in
          other entities which result in changes in Beneficial or Constructive
          Ownership of Series C Preferred Stock), and whether such transfer has
          occurred by operation of law or otherwise.

              "Trust" shall mean each of the trusts provided for in Section
               -----                                                       
          7(c) of these Articles Supplementary.

              "Trustee" shall mean any Person unaffiliated with the Company, or
               -------                                                         
          a Purported Beneficial Transferee, or a Purported Record Transferee,
          that is appointed by the Company to serve as trustee of a Trust.

          (b) Restriction on Ownership and Transfers.
              -------------------------------------- 

              (i)     Prior to the Restriction Termination Date:

                      (A) except as provided in Section 7(i) of these Articles
              Supplementary, no Person shall Beneficially Own Series C Preferred
              Stock which, taking into account any other capital stock of the
              Company Beneficially Owned by such Person, would cause such
              ownership to exceed the Beneficial Ownership Limit;

                      (B) except as provided in Section 7(i) of these Articles
              Supplementary, no Person shall Constructively Own Series C
              Preferred Stock which, taking into account any other capital stock
              of the Company Constructively Owned by such Person, would cause
              such ownership to exceed the Constructive Ownership Limit;

                      (C) no Person shall Beneficially or Constructively Own
              Series C Preferred Stock which, taking into account any other
              capital stock of the Company Beneficially or Constructively Owned
              by such Person, would result in the Company being "closely held"
              within the meaning of Section 856(h) of the Code, or otherwise
              failing to qualify as a REIT (including but not limited to
              Beneficial or Constructive Ownership that would result in the

                                       12
<PAGE>
 
              Company owning (actually or Constructively) an interest in a
              tenant that is described in Section 856(d)(2)(B) of the Code if
              the income derived by the Company (either directly or indirectly
              through one or more partnerships) from such tenant would cause the
              Company to fail to satisfy any of the gross income requirements of
              Section 856(c) of the Code or comparable provisions of state law).

              (ii)    If, prior to the Restriction Termination Date, any
Transfer (whether or not such Transfer is the result of a transaction entered
into through the facilities of the New York Stock Exchange ("NYSE")) or other
                                                             ----
event occurs that, if effective, would result in any Person Beneficially or
Constructively Owning Series C Preferred Stock in violation of Section 7(b)(i)
of these Articles Supplementary, (1) then that number of shares of Series C
Preferred Stock that otherwise would cause such Person to violate Section
7(b)(i) of these Articles Supplementary (rounded up to the nearest whole share)
shall be automatically transferred to a Trust for the benefit of a Charitable
Beneficiary, as described in Section 7(c), effective as of the close of business
on the business day prior to the date of such Transfer or other event, and such
Purported Beneficial Transferee shall thereafter have no rights in such shares
or (2) if, for any reason, the transfer to the Trust described in clause (1) of
this sentence is not automatically effective as provided therein to prevent any
Person from Beneficially or Constructively Owning Series C Preferred Stock in
violation of Section 7(b)(i) of these Articles Supplementary, then the Transfer
of that number of shares of Series C Preferred Stock that otherwise would cause
any Person to violate Section 7(b)(i) shall be void ab initio, and the Purported
Beneficial Transferee shall have no rights in such shares.

              (ii)    Subject to Section 7(n) of this Article Third and
notwithstanding any other provisions contained herein, prior to the Restriction
Termination Date, any Transfer of Series C Preferred Stock (whether or not such
Transfer is the result of a transaction entered into through the facilities of
the NYSE) that, if effective, would result in the capital stock of the Company
being beneficially owned by less than 100 Persons (determined without reference
to any rules of attribution) shall be void ab initio, and the intended
transferee shall acquire no rights in such Series C Preferred Stock.

It is expressly intended that the restrictions on ownership and Transfer
described in this Section 7(b) shall apply to the exchange rights provided in
Section 17.7 of the Partnership Agreement. Notwithstanding any of the provisions
of the Partnership Agreement to the contrary, a partner of the Operating
Partnership shall not be entitled to effect an exchange of an interest in the
Operating Partnership for Series C Preferred Stock if the actual or beneficial
or Beneficial or Constructive Ownership of Series C Preferred Stock would be
prohibited under the provisions of this Section 7.

          (c) Transfers of Series C Preferred Stock in Trust.
              ---------------------------------------------- 

              (i)     Upon any purported Transfer or other event described in
Section 7(b)(ii) of these Articles Supplementary, such Series C Preferred Stock
shall be deemed to have been transferred to the Trustee in his capacity as
trustee of a Trust for the exclusive

                                       13
<PAGE>
 
benefit of one or more Charitable Beneficiaries. Such transfer to the Trustee
shall be deemed to be effective as of the close of business on the business day
prior to the purported Transfer or other event that results in a transfer to the
Trust pursuant to Section 7(b)(ii). The Trustee shall be appointed by the
Company and shall be a Person unaffiliated with the Company, any Purported
Beneficial Transferee, or any Purported Record Transferee. Each Charitable
Beneficiary shall be designated by the Company as provided in Section 7(c)(vi)
of these Articles Supplementary.

              (ii)    Series C Preferred Stock held by the Trustee shall be
issued and outstanding Series C Preferred Stock of the Company. The Purported
Beneficial Transferee or Purported Record Transferee shall have no rights in the
shares of the Series C Preferred Stock held by the Trustee. The Purported
Beneficial Transferee or Purported Record Transferee shall not benefit
economically from ownership of any shares held in trust by the Trustee, shall
have no rights to dividends and shall not possess any rights to vote or other
rights attributable to the shares of Series C Preferred Stock held in the Trust.

              (iii)   The Trustee shall have all voting rights and rights to
dividends with respect to Series C Preferred Stock held in the Trust, which
rights shall be exercised for the exclusive benefit of the Charitable
Beneficiary.  Any dividend or distribution paid prior to the discovery by the
Company that shares of Series C Preferred Stock have been transferred to the
Trustee shall be paid to the Trustee upon demand, and any dividend or
distribution declared but unpaid shall be paid when due to the Trustee with
respect to such Series C Preferred Stock.  Any dividends or distributions so
paid over to the Trustee shall be held in trust for the Charitable Beneficiary.

          The Purported Record Transferee and Purported Beneficial Transferee
shall have no voting rights with respect to the Series C Preferred Stock held in
the Trust and, subject to Maryland law, effective as of the date the Series C
Preferred Stock has been transferred to the Trustee, the Trustee shall have the
authority (at the Trustee's sole discretion) (i) to rescind as void any vote
cast by a Purported Record Transferee with respect to such Series C Preferred
Stock prior to the discovery by the Company that the Series C Preferred Stock
has been transferred to the Trustee and (ii) to recast such vote in accordance
with the desires of the Trustee acting for the benefit of the Charitable
Beneficiary; provided, however, that if the Company has already taken
irreversible corporate action, then the Trustee shall not have the authority to
rescind and recast such vote.  Notwithstanding any other provision of these
Articles Supplementary to the contrary, until the Company has received
notification that the Series C Preferred Stock has been transferred into a
Trust, the Company shall be entitled to rely on its share transfer and other
stockholder records for purposes of preparing lists of stockholders entitled to
vote at meetings, determining the validity and authority of proxies and
otherwise conducting votes of stockholders.

              (iv)    Within 20 days of receiving notice from the Company that
shares of Series C Preferred Stock have been transferred to the Trust, the
Trustee of the Trust shall sell the shares of Series C Preferred Stock held in
the Trust to a Person, designated by the Trustee, whose ownership of the shares
of Series C Preferred Stock will not violate the ownership

                                       14
<PAGE>
 
limitations set forth in Section 7(b)(i). Upon such sale, the interest of the
Charitable Beneficiary in the shares of Series C Preferred Stock sold shall
terminate and the Trustee shall distribute the net proceeds of the sale to the
Purported Record Transferee and to the Charitable Beneficiary as provided in
this Section 7(c)(iv). The Purported Record Transferee shall receive the lesser
of (1) the price paid by the Purported Record Transferee for the shares of
Series C Preferred Stock in the transaction that resulted in such transfer to
the Trust (or, if the event which resulted in the transfer to the Trust did not
involve a purchase of such shares of Series C Preferred Stock at Market Price,
the Market Price of such shares of Series C Preferred Stock on the day of the
event which resulted in the transfer of such shares of Series C Preferred Stock
to the Trust) and (2) the price per share received by the Trustee (net of any
commissions and other expenses of sale) from the sale or other disposition of
the shares of Series C Preferred Stock held in the Trust. Any net sales proceeds
in excess of the amount payable to the Purported Record Transferee shall be
immediately paid to the Charitable Beneficiary together with any dividends or
other distributions thereon. If, prior to the discovery by the Company that
shares of such Series C Preferred Stock have been transferred to the Trustee,
such shares of Series C Preferred Stock are sold by a Purported Record
Transferee then (i) such shares of Series C Preferred Stock shall be deemed to
have been sold on behalf of the Trust and (ii) to the extent that the Purported
Record Transferee received an amount for such shares of Series C Preferred Stock
that exceeds the amount that such Purported Record Transferee was entitled to
receive pursuant to this Section 7(c)(iv), such excess shall be paid to the
Trustee upon demand.

              (v)     Series C Preferred Stock transferred to the Trustee shall
be deemed to have been offered for sale to the Company, or its designee, at a
price per share equal to the lesser of (i) the price paid by the Purported
Record Transferee for the shares of Series C Preferred Stock in the transaction
that resulted in such transfer to the Trust (or, if the event which resulted in
the transfer to the Trust did not involve a purchase of such shares of Series C
Preferred Stock at Market Price, the Market Price of such shares of Series C
Preferred Stock on the day of the event which resulted in the transfer of such
shares of Series C Preferred Stock to the Trust) and (ii) the Market Price on
the date the Company, or its designee, accepts such offer. The Company shall
have the right to accept such offer until the Trustee has sold the shares of
Series C Preferred Stock held in the Trust pursuant to Section 7(c)(iv). Upon
such a sale to the Company, the interest of the Charitable Beneficiary in the
shares of Series C Preferred Stock sold shall terminate and the Trustee shall
distribute the net proceeds of the sale to the Purported Record Transferee and
any dividends or other distributions held by the Trustee with respect to such
Series C Preferred Stock shall thereupon be paid to the Charitable Beneficiary.

              (vi)    By written notice to the Trustee, the Company shall
designate one or more nonprofit organizations to be the Charitable Beneficiary
of the interest in the Trust such that the Series C Preferred Stock held in the
Trust would not violate the restrictions set forth in Section 7(b)(i) in the
hands of such Charitable Beneficiary.

          (d) Remedies For Breach.  If the Board of Directors or a committee
              -------------------                                           
thereof or other designees if permitted by the MGCL shall at any time determine
in good faith that a Transfer or other event has taken place in violation of
Section 7(b) of these Articles

                                       15
<PAGE>
 
Supplementary or that a Person intends to acquire, has attempted to acquire or
may acquire beneficial ownership (determined without reference to any rules of
attribution), Beneficial Ownership or Constructive Ownership of any shares of
Series C Preferred Stock of the Company in violation of Section 7(b) of these
Articles Supplementary, the Board of Directors or a committee thereof or other
designees if permitted by the MGCL shall take such action as it deems advisable
to refuse to give effect or to prevent such Transfer, including, but not limited
to, causing the Company to redeem shares of Series C Preferred Stock, refusing
to give effect to such Transfer on the books of the Company or instituting
proceedings to enjoin such Transfer; provided, however, that any Transfers (or,
in the case of events other than a Transfer, ownership or Constructive Ownership
or Beneficial Ownership) in violation of Section 7(b)(i) of these Articles
Supplementary, shall automatically result in the transfer to a Trust as
described in Section 7(b)(ii) and any Transfer in violation of Section 7(b)(iii)
shall automatically be void ab initio irrespective of any action (or non-action)
by the Board of Directors.

          (e) Notice of Restricted Transfer.  Any Person who acquires or
              -----------------------------                             
attempts to acquire shares of Series C Preferred Stock in violation of Section
7(b) of these Articles Supplementary, or any Person who is a Purported
Beneficial Transferee such that an automatic transfer to a Trust results under
Section 7(b)(ii) of these Articles Supplementary, shall immediately give written
notice to the Company of such event and shall provide to the Company such other
information as the Company may request in order to determine the effect, if any
of such Transfer or attempted Transfer on the Company's status as a REIT.

          (f) Owners Required To Provide Information.  Prior to the Restriction
              --------------------------------------                           
Termination Date each Person who is a beneficial owner or Beneficial Owner or
Constructive Owner of Series C Preferred Stock and each Person (including the
shareholder of record) who is holding Series C Preferred Stock for a beneficial
owner or Beneficial Owner or Constructive Owner shall provide to the Company
such information that the Company may request, in good faith, in order to
determine the Company's status as a REIT.

          (g) Remedies Not Limited.  Nothing contained in these Articles
              --------------------                                      
Supplementary (but subject to Section 7(n) of these Articles Supplementary)
shall limit the authority of the Board of Directors to take such other action as
it deems necessary or advisable to protect the Company and the interests of its
shareholders by preservation of the Company's status as a REIT.

          (h) Ambiguity.  In the case of an ambiguity in the application of any
              ---------                                                        
of the provisions of this Section 7 of these Articles Supplementary, including
any definition contained in Section 7(a), the Board of Directors shall have the
power to determine the application of the provisions of this Section 7 with
respect to any situation based on the facts known to it (subject, however, to
the provisions of Section 7(n) of these Articles Supplementary).  In the event
Section 7 requires an action by the Board of Directors and these Articles
Supplementary fail to provide specific guidance with respect to such action, the
Board of Directors shall have the power to determine the action to be taken so
long as such action is not contrary to the provisions of Section 7.  Absent a
decision to the contrary by the Board of Directors (which the Board of

                                       16
<PAGE>
 
Directors may make in its sole and absolute discretion), if a Person would have
(but for the remedies set forth in Section 7(b)) acquired Beneficial or
Constructive Ownership of Series C Preferred Stock in violation of Section
7(b)(i), such remedies (as applicable) shall apply first to the shares of Series
C Preferred Stock which, but for such remedies, would have been actually owned
by such Person, and second to shares of Series C Preferred Stock, which, but for
such remedies, would have been Beneficially Owned or Constructively Owned (but
not actually owned) by such Person, pro rata among the Persons who actually own
such shares of Series C Preferred Stock based upon the relative number of the
shares of Series C Preferred Stock held by each such Person.

          (i)  Exceptions.
               ---------- 

              (i)     Subject to Section 7(b)(i)(C), the Board of Directors, in
its sole discretion, may exempt a Person from the limitation on a Person
Beneficially Owning shares of Series C Preferred Stock in violation of Section
7(b)(i)(A) if the Board of Directors obtains such representations and
undertakings from such Person as are reasonably necessary in the opinion of the
Board of Directors to ascertain that no individual's Beneficial Ownership of
such shares of Series C Preferred Stock will violate Section 7(b)(i)(A) or that
any such violation will not cause the Company to fail to qualify as a REIT under
the Code, and agrees that any violation of such representations or undertakings
(or other action which is contrary to the restrictions contained in Section 7(b)
of these Articles Supplementary) or attempted violation will result in such
Series C Preferred Stock being transferred to a Trust in accordance with Section
7(b)(ii) of the Articles Supplementary.

              (ii)    Subject to Section 7(b)(i)(C), the Board of Directors, in
its sole discretion, may exempt a Person from the limitation on a Person
Constructively Owning Series C Preferred Stock in violation of Section
7(b)(i)(B), if the Company obtains such representations and undertakings from
such Person as are reasonably necessary in the opinion of the Board of Directors
to ascertain that such Person does not and will not own, actually or
Constructively, an interest in a tenant of the Company (or a tenant of any
entity owned in whole or in part by the Company) that would cause the Company to
own, actually or Constructively more than a 9.8% interest (as set forth in
Section 856(d)(2)(B) of the Code) in such tenant and that any violation or
attempted violation will result in such Series C Preferred Stock being
transferred to a Trust in accordance with Section 7(b)(ii) of these Articles
Supplementary.  Notwithstanding the foregoing, the inability of a Person to make
the certification described in this Section 7(i)(ii) shall not prevent the Board
of Directors, in its sole discretion, from exempting such Person from the
limitation on a Person Constructively Owning Series C Preferred Stock in
violation of Section 7(b)(i)(B) if the Board of Directors determines that the
resulting application of Section 856(d)(2)(B) of the Code would affect the
characterization of less than 0.5% of the gross income (as such term is used in
Section 856(c)(2) of the Code) of the Company in any taxable year, after taking
into account the effect of this sentence with respect to all other capital stock
of the Company to which this sentence applies.

                                       17
<PAGE>
 
              (iii)   Prior to granting any exception pursuant to Section
7(i)(i) or (ii) of these Articles Supplementary, the Board of Directors may
require a ruling from the Internal Revenue Service, or an opinion of counsel, in
either case in form and substance satisfactory to the Board of Directors in its
sole discretion, as it may deem necessary or advisable in order to determine or
ensure the Company's status as a REIT.

          (j) Legends.  Each certificate for Series C Preferred Stock shall bear
              -------                                                           
substantially the following legends in addition to any legends required to
comply with federal and state securities laws:

                                 CLASS OF STOCK

          "THE COMPANY IS AUTHORIZED TO ISSUE CAPITAL STOCK OF MORE THAN ONE
          CLASS, CONSISTING OF COMMON STOCK AND ONE OR MORE CLASSES OF PREFERRED
          STOCK.  THE BOARD OF DIRECTORS IS AUTHORIZED TO DETERMINE THE
          PREFERENCES, LIMITATIONS AND RELATIVE RIGHTS OF ANY CLASS OF THE
          PREFERRED STOCK BEFORE THE ISSUANCE OF SHARES OF SUCH CLASS OF
          PREFERRED STOCK.  THE COMPANY WILL FURNISH, WITHOUT CHARGE, TO ANY
          STOCKHOLDER MAKING A WRITTEN REQUEST THEREFOR, A COPY OF THE COMPANY'S
          CHARTER AND A WRITTEN STATEMENT OF THE DESIGNATIONS, RELATIVE RIGHTS,
          PREFERENCES, CONVERSION OR OTHER RIGHTS, VOTING POWERS, RESTRICTIONS,
          LIMITATIONS AS TO DIVIDENDS AND OTHER DISTRIBUTIONS, QUALIFICATIONS
          AND TERMS AND CONDITIONS OF REDEMPTION OF THE STOCK OF EACH CLASS
          WHICH THE COMPANY HAS THE AUTHORITY TO ISSUE AND, IF THE COMPANY IS
          AUTHORIZED TO ISSUE ANY PREFERRED OR SPECIAL CLASS AND SERIES, (i) THE
          DIFFERENCES IN THE RELATIVE RIGHTS AND PREFERENCES BETWEEN THE SHARES
          OF EACH SERIES TO THE EXTENT SET, AND (ii) THE AUTHORITY OF THE BOARD
          OF DIRECTORS TO SET SUCH RIGHTS AND PREFERENCES OF SUBSEQUENT SERIES.
          REQUESTS FOR SUCH WRITTEN STATEMENT MAY BE DIRECTED TO THE SECRETARY
          OF THE COMPANY AT ITS PRINCIPAL OFFICE."

                     RESTRICTION ON OWNERSHIP AND TRANSFER

          "THE SHARES OF SERIES C PREFERRED STOCK REPRESENTED BY THIS
          CERTIFICATE ARE SUBJECT TO RESTRICTIONS ON BENEFICIAL AND CONSTRUCTIVE
          OWNERSHIP AND TRANSFER FOR THE PURPOSE OF THE COMPANY'S MAINTENANCE OF
          ITS STATUS AS A REAL ESTATE INVESTMENT TRUST UNDER THE INTERNAL
          REVENUE CODE OF 1986, AS AMENDED (THE "CODE").  SUBJECT TO CERTAIN
          FURTHER RESTRICTIONS AND EXCEPT AS EXPRESSLY PROVIDED IN

                                       18
<PAGE>
 
          THE ARTICLES SUPPLEMENTARY FOR THE SERIES C PREFERRED STOCK, (i) NO
          PERSON MAY BENEFICIALLY OWN SHARES OF THE COMPANY'S SERIES C PREFERRED
          STOCK WHICH, TAKING INTO ACCOUNT ANY OTHER CAPITAL STOCK OF THE
          COMPANY BENEFICIALLY OWNED BY SUCH PERSON, WOULD CAUSE SUCH OWNERSHIP
          TO EXCEED THE BENEFICIAL OWNERSHIP LIMIT OF 7.0%; (ii) NO PERSON MAY
          CONSTRUCTIVELY OWN SHARES OF THE COMPANY'S SERIES C PREFERRED STOCK
          WHICH, TAKING INTO ACCOUNT ANY OTHER CAPITAL STOCK OF THE COMPANY
          CONSTRUCTIVELY OWNED BY SUCH PERSON, WOULD CAUSE SUCH OWNERSHIP TO
          EXCEED THE CONSTRUCTIVE OWNERSHIP LIMIT OF 9.8%; (iii) NO PERSON MAY
          BENEFICIALLY OR CONSTRUCTIVELY OWN SERIES C PREFERRED STOCK THAT,
          TAKING INTO ACCOUNT ANY OTHER CAPITAL STOCK OF THE COMPANY
          BENEFICIALLY OR CONSTRUCTIVELY OWNED BY SUCH PERSON, WOULD RESULT IN
          THE COMPANY BEING "CLOSELY HELD" UNDER SECTION 856(h) OF THE CODE OR
          OTHERWISE CAUSE THE COMPANY TO FAIL TO QUALIFY AS A REIT; AND (iv) NO
          PERSON MAY TRANSFER SERIES C PREFERRED STOCK IF SUCH TRANSFER WOULD
          RESULT IN THE CAPITAL STOCK OF THE COMPANY BEING OWNED BY FEWER THAN
          100 PERSONS. ANY PERSON WHO BENEFICIALLY OR CONSTRUCTIVELY OWNS OR
          ATTEMPTS TO BENEFICIALLY OR CONSTRUCTIVELY OWN SERIES C PREFERRED
          STOCK WHICH CAUSES OR WILL CAUSE A PERSON TO BENEFICIALLY OR
          CONSTRUCTIVELY OWN SERIES C PREFERRED STOCK IN EXCESS OF THE ABOVE
          LIMITATIONS MUST IMMEDIATELY NOTIFY THE COMPANY. IF ANY OF THE
          RESTRICTIONS ON TRANSFER OR OWNERSHIP ARE VIOLATED, THE SERIES C
          PREFERRED STOCK REPRESENTED HEREBY WILL BE AUTOMATICALLY TRANSFERRED
          TO THE TRUSTEE OF A TRUST FOR THE BENEFIT OF ONE OR MORE CHARITABLE
          BENEFICIARIES. IN ADDITION, THE COMPANY MAY REDEEM SHARES UPON THE
          TERMS AND CONDITIONS SPECIFIED BY THE BOARD OF DIRECTORS IN ITS SOLE
          DISCRETION IF THE BOARD OF DIRECTORS DETERMINES THAT OWNERSHIP OR A
          TRANSFER OR OTHER EVENT MAY VIOLATE THE RESTRICTIONS DESCRIBED ABOVE.
          FURTHERMORE, UPON THE OCCURRENCE OF CERTAIN EVENTS, ATTEMPTED
          TRANSFERS IN VIOLATION OF THE RESTRICTIONS DESCRIBED ABOVE MAY BE VOID
          AB INITIO. ALL TERMS IN THIS LEGEND WHICH ARE DEFINED IN THE ARTICLES
          SUPPLEMENTARY FOR THE SERIES C PREFERRED STOCK SHALL HAVE THE MEANINGS
          ASCRIBED TO THEM IN SUCH ARTICLES SUPPLEMENTARY, AS THE SAME MAY BE
          AMENDED FROM TIME TO TIME, A COPY OF WHICH, INCLUDING THE RESTRICTIONS
          ON TRANSFER AND OWNERSHIP, WILL BE FURNISHED TO EACH HOLDER

                                       19
<PAGE>
 
          OF SERIES C PREFERRED STOCK ON REQUEST AND WITHOUT CHARGE. REQUESTS
          FOR SUCH A COPY MAY BE DIRECTED TO THE SECRETARY OF THE COMPANY AT ITS
          PRINCIPAL OFFICE."

          (k) Exchange of Series C Preferred Units.  So long as the Company
              ------------------------------------                         
remains the general partner of the Operating Partnership, the Board of Directors
of the Company is hereby expressly vested with authority (subject to the
restrictions on ownership, transfer and redemption of Series C Preferred Stock
set forth in this Section 7) to issue, and shall issue to the extent provided in
the Partnership Agreement, Series C Preferred Stock in exchange for Series C
Preferred Units (as defined in the Partnership Agreement) (the "Series C
                                                                --------
Preferred Units").
---------------   

          (l) Reservation of Shares.  Pursuant to the obligations of the Company
              ---------------------                                             
under the Partnership Agreement to issue Series C Preferred Stock in exchange
for Series C Preferred Units, the Board of Directors is hereby required to
reserve and authorize for issuance a number of authorized but unissued shares of
Series C Preferred Stock not less than the number of Series C Preferred Units
issued to permit the Company to issue Series C Preferred Stock in exchange for
Series C Preferred Units that may be exchanged for or converted into Series C
Preferred Stock as provided in the Partnership Agreement.

          (m) Severability.  If any provision of this Section 7 or any
              ------------                                            
application of any such provision is determined to be invalid by any Federal or
state court having jurisdiction over the issues, the validity of the remaining
provisions shall not be affected and other applications of such provision shall
be affected only to the extent necessary to comply with the determination of
such court.

          (n) NYSE.  Nothing in this Section 7 shall preclude the settlement of
              ----                                                             
any transaction entered into through the facilities of the NYSE.  The shares of
Series C Preferred Stock that are the subject of such transaction shall continue
to be subject to the provisions of this Section 7 after such settlement.

          (o) Applicability of Section 7.  The provisions set forth in this
              --------------------------                                   
Section 7 shall apply to the Series C Preferred Stock notwithstanding any
contrary provisions of the Series C Preferred Stock provided for elsewhere in
these Articles Supplementary.

          Section 8.  No Conversion Rights.  The holders of the Series C
                      --------------------                              
Preferred Stock shall not have any rights to convert such shares into shares of
any other class or series of stock or into any other securities of, or interest
in, the Company.

          Section 9.  No Sinking Fund.  No sinking fund shall be established
                      ---------------                                       
for the retirement or redemption of Series C Preferred Stock.

          Section 10. No Preemptive Rights.  No holder of the Series C
                      --------------------                            
Preferred Stock of the Company shall, as such holder, have any preemptive rights
to purchase or subscribe for

                                       20
<PAGE>
 
additional shares of stock of the Company or any other security of the Company
which it may issue or sell.

          FOURTH:   The Series C Preferred Stock have been classified and
          ------                                                         
designated by the Board of Directors under the authority contained in the
Charter.

          FIFTH:    These Articles Supplementary have been approved by the Board
          -----                                                                 
of Directors in the manner and by the vote required by law.

          SIXTH:    The Articles Supplementary shall be effective at the time
          -----                                                              
the State Department of Assessments and Taxation of Maryland accepts these
Articles Supplementary for the record.

          SEVENTH:  The undersigned Vice President of the Company acknowledges
          -------                                                             
these Articles Supplementary to be the act of the Company and, as to all matters
or facts required to be verified under oath, the undersigned Vice President
acknowledges that to the best of his knowledge, information and belief, these
matters and facts are true in all material respects and that this statement is
made under the penalties for perjury.

                                       21
<PAGE>
 
          IN WITNESS WHEREOF, the Company has caused these Articles
Supplementary to be executed under seal in its name and on its behalf by its
Senior Vice President and attested to by its Secretary on this 24th day of
November, 1998.

                              KILROY REALTY CORPORATION

                              By:    /s/ Tyler H. Rose
                                 -------------------------
                                 Tyler H. Rose
                                 Senior Vice President

[SEAL]

ATTEST:

 
/s/ Richard E. Moran Jr.
------------------------
Richard E. Moran Jr.
Secretary

                                      S-1
