
<PAGE>
 
                                                                     EXHIBIT 3.1

                           KILROY REALTY CORPORATION

                            ARTICLES SUPPLEMENTARY

                               1,500,000 SHARES 

             8.075% SERIES A 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 (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 resolutions duly adopted on February 5, 1998 has classified 1,500,000 shares 
of the authorized but unissued Preferred Stock par value $.01 per share 
("PREFERRED STOCK") as a separate class of Preferred Stock, authorized the 
  ---------------
issuance of a maximum of 1,500,00 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 "8.075% Series A 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 8.075% Series A
Cumulative Redeemable Preferred Stock (to the extent not set by the Board of 
Directors in the resolutions referred to in Article FIRST of these Articles 
                                                    -----
Supplementary) and authorizing the issuance of up to 1,500,000 shares of 8.075% 
Series A Cumulative Redeemable Preferred Stock.
 
<PAGE>
 

                                       2



          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 
limitation 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 "8.075% Series A Cumulative Redeemable Preferred Stock" (the 
"SERIES A PREFERRED STOCK") is hereby established. The number of shares of 
--------------------------
Series A Preferred Stock shall be 1,500,000.


         SECTION 2.  RANK. The Series A Preferred Stock will, with respect to 
                     ----
distributions or rights upon voluntary or involuntary liquidation, winding-up or
dissolution of the Company, or both, rank senior to all classes or series of
Common Stock (ad defined in the Charter) and to all classes or series of equity
securities of the Company now or hereafter authorized, issued or outstanding,
other than any class or series of equity securities of the Company expressly
designated as ranking on a parity with or senior to the Series A 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 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 A 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 A 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 od distributions 
and holders of equity securities ranking senior to the Series A Preferred Stock
as to payment of distributions, holders of Series A 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 8.075% of the $50.00 liquidation 
preference per share of Series A Preferred Stock. Such distributions shall be 
cumulative, shall accrue from the original date of issuance and will be payable 
quarterly in arrears, on or before the 15th of February, May, August and 
November of each year and, in the event of a redemption, on the redemption dates
(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 months and for any 
period shorter than a full quarterly period for which distributions are 
computed, the amount of the distribution 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


                         
<PAGE>
 
                                       3


made on the Series A 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 A Preferred Stock will be made to the
holders of record of the Series A 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
                                   ------------------------
anything to the contrary set forth herein, each share of Series A Preferred
Stock shall also continue to accrue all accrued and unpaid distributions up to
the exchange date on any Series A Preference Unit (as defined in the Second
Amended and Restated Limited Partnership Agreement of Kilroy Realty, L.P. dated
as of February 6, 1998 (the "SECOND AMENDMENT")) validly exchanged into such
                             ----------------
share of Series A Preferred Stock in accordance with the provisions of such
Second Amendment.

       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 A 
            ---------------------------
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 A 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
of such distributions and whether or not such distributions are authorized.
Accrued but unpaid distributions on the Series A 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. (i) So long as any Series A 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 (such Common Stock or other junior stock, collectively, "JUNIOR
                                                                         ------
      

<PAGE>
 
                                       4

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 A
Preferred Stock, any Parity Preferred Stock with respect to distributions or any
Junior Stock, unless, in each case, all distributions accumulated on all Series
A 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 A Preferred Stock as to distributions, and
(iii) purchase by the Company of such Series A Preferred Stock, Parity Preferred
Stock with respect to distributions or Junior Stock pursuant to Article IV.E. of
the Charter with respect to the Common Stock 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 A
Preferred Stock, all distributions authorized and declared on the Series A
Preferred Stock and all classes or series of outstanding Parity Preferred Stock
with respect to distributions shall be authorized and declared so that the
amount of distributions authorized and declared per share of Series A Preferred
Stock and such other classes or series of Parity Preferred Stock shall in all
cases bear to each other the same ratio that accrued distributions per share on
the Series A Preferred Stock and such other classes or series of Parity
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 A 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.

     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 A Preferred Stock with respect to rights upon any voluntary or
involuntary liquidation, dissolution or winding-up of the Company, the holders
of Series A Preferred Stock shall be entitled to receive out of the assets of
the Company, the holders of Series A 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 A 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 A 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
<PAGE>
 
                                       5

distributions to the holders of Series A 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 A Preferred 
Stock and such Parity Preferred Stock shall be made so that the payments on the 
Series A 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 A 
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 than 60 days prior 
to the payment date stated therein, to each record holder of the Series A 
Preferred Stock at the respective addresses of such holders as the same shall 
appear on the same 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 A 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 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
               -------------------      ----------------------------
A Preferred Stock may not, subject to SECTION 7 hereof, be redeemed prior to 
February 6, 2003.  On or after such date, the Company shall have the right to 
redeem the Series A 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 A Preferred 
Stock plus accumulated and unpaid distributions to the date of redemption. If 
fewer than all of the outstanding shares of Series A Preferred Stock are to be 
redeemed, the shares of



<PAGE>
 
                                       6

Series A 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 A 
        ------------------------
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 A Preferred Stock unless all accumulated
and unpaid distributions have been paid on all Series A 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 A 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 A 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 A 
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 A Preferred Stock to be redeemed, (iv) the place or places 
where such shares of Series A Preferred Stock are to be surrendered for payment 
of the redemption price, (v) that distributions on the Series A Preferred 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 A Preferred Stock. 
If fewer than all of the shares of Series A 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 A Preferred Stock held by such holder to be redeemed.

        (ii) If the Company gives a notice of redemption in respect of Series A 
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 A 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 A Preferred Stock upon surrender of the 
Series A Preferred Stock by such holders at the place

<PAGE>
 
                                       7

designated in the notice of redemption. On and after the date of redemption, 
distributions will cease to accumulate on the Series A Preferred Stock or 
portions thereof called for redemption, unless the Company defaults in the 
payment thereof. If any date fixed for redemption of Series A 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 A Preferred 
Stock is improperly withheld or refused and not paid by the Company, 
distributions on such Series A 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 A 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 A Preferred
               -------------      -------
Stock will not have any voting rights, except as set forth below.

    (b) Right to Elect Directors. If at any time full distributions shall not 
        ------------------------
have been timely made on any Series A Preferred Stock with respect to any six 
(6) prior quarterly distribution periods, whether or not consecutive, (a 
"Preferred Distribution Default"), the holders such Series A 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, will have the right to elect two additional directors to serve on 
the Company's Board of Directors (the "Preferred Stock Directors") at a special
                                       -------------------------
meeting called by the holders of record of at least 10% of the outstanding 
shares of Series A Preferred Stock or any such class or series of Parity 
Preferred Stock 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 A Preferred Stock and each such class or 
series of Parity Preferred Stock have been paid in full. A distribution in 
respect of Series A 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. If and when all
accumulated distributions and the distribution for the current distribution 
period on the Series A Preferred Stock shall have been paid in full or set aside
for payment in full, the holders of the Series A Preferred Stock shall be 
divested of the voting rights set forth in Section

<PAGE>

                                      8
 
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
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 A 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 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 A 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 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 A Preferred Stock remains
          ---------------------
outstanding, the Company shall not, without the affirmative vote of the holders 
of at least two-thirds of the Series A 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 A 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 a 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 By-laws, 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 A 
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 A Preferred Stock remains outstanding
with the terms thereof unchanged, or (b) the resulting, surviving or transferee
entity is a corporation organized under the laws of any state and substitutes
the Series A Preferred Stock for other preferred stock having substantially the
same terms and same rights as the Series A 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
materially and adversely affect such rights, privileges or voting powers of the
holders of the Series A Preferred Stock and provided further that any increase
in

<PAGE>
 
                                       9

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 A 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 A Preferred Stock with respect to payment of
distributions or the distribution of assets upon liquidation, dissolution or
winding-up to the extent such Preferred Stock is not issued to a 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 this Section 7 of these 
                -----------
Articles Supplementary, the following terms shall have the following meanings:

                "Beneficial Ownership" shall mean ownership of Series A 
                 --------------------
          Preferred Stock by a Person who is or would be treated as an owner of
          such Series A 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 capital stock 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) or 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 A 
                  -----------------------
          Preferred Stock by a Person who is or would be treated as an owner of
          such Series A 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.

<PAGE>

                                      10
 
    "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 A Preferred Stock on the trading day 
immediately preceding the relevant date, or if the Series A Preferred Stock is 
not then traded on the New York Stock Exchange, the last reported sales price of
the Series A Preferred Stock on the trading day immediately preceding the 
relevant date as reported on any exchange or quotation system over which the 
Series A Preferred Stock may be traded, or if the Series A Preferred Stock is 
not then traded over any exchange or quotation system, then the market price of 
the Series A 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 A Preferred Stock provided that the ownership of such shares of Series A 
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
<PAGE>

                                      11
 
or owned shares of Series A 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 A 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.

      "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 A Preferred Stock, (including (i) the granting of 
any option or entering into any agreement for the sale, transfer or other 
disposition of Series A Preferred Stock or (ii) the sale, transfer, assignment 
or other disposition of any securities (or rights convertible into or 
exchangeable for Series A 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 results in changes in Beneficial or Constructive Ownership of
Series A 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.
<PAGE>

                                      12
 
      (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 A 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 A 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 A 
          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 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 A Preferred Stock in violation of Section 7(b)(i)
of these Articles Supplementary, (1) then that number of shares of Series A
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 A Preferred Stock in
violation of Section 7(b)(i) of these Articles Supplementary, then the
<PAGE>
 
                                      13

Transfer of that number of shares of Series A Preferred Stock that otherwise 
would cause any Person to violate Section 7(b)(1) shall be void ab initio, and 
the Purported Beneficial Transferee shall have no rights in such shares.

          (iii)  Notwithstanding any other provisions contained herein, prior to
the Restriction Termination Date, any Transfer of Series A 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 A
Preferred Stock.

          (iv)  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 16.7 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 A Preferred Stock if the actual or
beneficial or Beneficial or Constructive Ownership of Series A Preferred Stock
would be prohibited under the provisions of this Section 7.

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

           (i)  Upon any purported Transfer or other event described in Section 
7(b)(ii) of these Articles Supplementary, such Series A Preferred Stock shall be
deemed to have been transferred to the Trustee in his capacity as trustee of a
Trust for the exclusive 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 A Preferred Stock held by the Trustee shall be issued
and outstanding Series A Preferred Stock of the Company. The Purported
Beneficial Transferee or Purported Record Transferee shall have no rights in
the shares of Series A 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 A Preferred Stock held in the Trust.

           (iii)  The Trustee shall have all voting rights and rights to 
dividends with respect to Series A Preferred Stock held in the Trust, which 
rights shall be exercised for the 

<PAGE>
 
                                      14

exclusive benefit of the Charitable Beneficiary. Any dividend or distribution
paid prior to the discovery by the Company that shares of Series A 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 A Preferred Stock. Any dividends
or distribution so paid over to the Trustee shall be held in trust for the
Charitable Beneficiary.

         The Purported Record Transferee and Purported Beneficial Tranferee 
shall have no voting rights with respect to the Series A Preferred Stock held in
the Trust and, subject to maryland law, effective as of the date the Series A 
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 A Preferred 
Stock prior to the discovery by the Company that the Series A 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 A 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 to stockholders.

         (iv)  Within 20 days of receiving notice from the Company that shares 
of Series A Preferred Stock have been transferred to the Trust, the Trustee of 
the Trust shall sell the shares of Series A Preferred Stock held in the Trust to
a Person, designated by the Trustee, whose ownership of the shares of Series A 
Preferred Stock will not violate the ownership limitations set forth in Section 
7(b)(i). Upon such sale, the interest of the Charitable beneficiary in the 
shares of Series A 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 A 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 A Preferred Stock at Market Price, the Market Price of such 
shares of Series A Preferred Stock on the day of the event which resulted in the
transfer of such shares of Series A 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 A 
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 A 
Preferred Stock have been transferred to the Trustee, such shares of Series A 
Preferred Stock are sold by a Purported Record Transferee then (i) such shares 
of Series A Preferred Stock shall be deemed to
<PAGE>
 
                                      15

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 A 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 A 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 A 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 A 
Preferred Stock at Market Price, the Market Price of such shares of Series A 
Preferred Stock on the day of the event which resulted in the transfer of such 
shares of Series A 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 A 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 A 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 A 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 (i) the Series A 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 and (ii) each charitable Beneficiary is an organization 
described in Sections 170(l)(A), 170(c)(2) or 501(c)(3) of the Code.

     (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 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 A 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 A 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
<PAGE>
 
                                      16

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 A 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 A Preferred Stock and each Person (including the
shareholder of record) who is holding Series A 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 provision 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 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 A Preferred Stock in violation of Section 7(b)(i), such 
remedies (as applicable) shall apply first to the shares of Series A Preferred 
Stock which, but for such remedies, would have been actually owned by such 
Person, and second to shares of Series A 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 A Preferred Stock based upon the relative number of the 
shares of Series A Preferred Stock held by each such Person.
<PAGE>

                                      17
 
       (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 A 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 to ascertain that no 
individual's Beneficial Ownership of such shares of Series A 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 A Preferred 
Stock being transferred to a Trust in accordance with Section 7(b)(ii) of these 
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 A Preferred Stock in violation of Section
7(b)(i)(B), if such Person does not and represents that it 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 the Company
obtains such representations and undertakings from such Person as are reasonably
necessary to ascertain this fact and agrees that any violation or attempted
violation will result in such Series A 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 A 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 and comparable
provisions of applicable state law 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.

             (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 A Preferred Stock shall bear 
             -------
the following legends:
<PAGE>
 
                                      18

                                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."

                    Restrictions on Ownership and Transfer

"THE SHARES OF SERIES A 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 THE ARTICLES SUPPLEMENTARY FOR THE SERIES A PREFERRED STOCK, (i) NO
PERSON MAY BENEFICIALLY OWN SHARES OF THE COMPANY'S SERIES A 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%; (ii) NO PERSON MAY CONSTRUCTIVELY OWN SHARES OF THE
COMPANY'S SERIES A PREFERRED STOCK WHICH, TAKING INTO


<PAGE>
                                      19
 
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 A 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 A 
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 A 
PREFERRED STOCK WHICH CAUSES OR WILL CAUSE A PERSON TO BENEFICIALLY OR 
CONSTRUCTIVELY OWN SERIES A 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 A 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 
DEFINED IN THE ARTICLES SUPPLEMENTARY FOR THE SERIES A PREFERRED STOCK SHALL 
HAVE THE MEANINGS ASCRIBED TO THEM IN THE ARTICLES SUPPLEMENTARY FOR THE SERIES 
A PREFERRED STOCK 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 OF SERIES A 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."
<PAGE>

                                      20
 
    (k) Exchange of Series A 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 A Preferred Stock set forth in
this Section 7) to issue, and shall issue to the extent provided in the 
     -------
Partnership Agreement, Series A Preferred Stock in exchange for Series A 
Preferred Units (as defined in the Partnership Agreement) (the "Series A 
                                                                -------- 
Preferred Units") 
---------------

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

    Section 8.  No Conversion Rights. The holders of the Series A 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 A Preferred Stock.

    Section 10. No Preemptive Rights. No holder of the Series A Preferred Stock
                --------------------
of the Company shall, as such holder, have any preemptive rights to purchase or 
subscribe for additional shares of stock of the Company or any other security of
the Company which it may issue or sell.

  
<PAGE>

                                      21
 
    FOURTH: The Series A 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 undersigned Vice President of the Company acknowledges these 
    -----
Articles Supplementary to be the corporate 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.

<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 6th day of February, 1998.

                                     KILROY REALTY CORPORATION

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

[SEAL]

ATTEST:

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



                  [SIGNATURE PAGE FOR ARTICLES SUPPLEMENTARY]
