
<PAGE>   1
                                                                    EXHIBIT 4.13




                                                     
                                                     
     NUMBER                                                       SHARES



                         CHANCELLOR MEDIA CORPORATION


                            INCORPORATED UNDER THE   
                        LAWS OF THE STATE OF DELAWARE



  SEE REVERSE FOR                                                 CUSIP
CERTAIN DEFINITIONS


THIS CERTIFIES THAT




is the owner of:



 FULLY PAID AND NON-ASSESSABLE SHARES OF THE 7% CONVERTIBLE PREFERRED STOCK,
                         PAR VALUE $.01 PER SHARE OF

======================== CHANCELLOR MEDIA CORPORATION ==========================


(the "Corporation"), a Delaware corporation. The shares represented by this
certificate are transferable only on the stock transfer books of the
Corporation by the holder of record hereof, or by his duly authorized attorney
or legal representative, upon the surrender of this certificate properly
endorsed. This certificate is not valid until countersigned and registered by 
the Corporation's transfer agent and registrar.

        IN WITNESS Whereof, the Corporation has caused this certificate to be 
executed by the facsimile signatures of its duly authorized officers and has
caused a facsimile of its corporate seal to be hereunto affixed.

Dated:          


THE FACSIMILE SIGNATURE OF                            THE FACSIMILE SIGNATURE OF
                                                                      
--------------------------                            --------------------------
     TO APPEAR HERE                                          TO APPEAR HERE 
                                                                      
        PRESIDENT                                          ASSISTANT SECRETARY
                                                                      

                         CHANCELLOR MEDIA CORPORATION
                               [CORPORATE SEAL]
                                   DELAWARE



Countersigned and Registered:                       Transfer Agent and Registrar
THE BANK OF NEW YORK                            By
 (New York)                                         Authorized Signature



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                         CHANCELLOR MEDIA CORPORATION

    This Certificate and the shares represented hereby are issued and shall be
subject to all the provisions of the Certificate of Incorporation and Bylaws of
the Corporation and the amendments from time to time made thereto, copies of
which are on file at the principal office of the Corporation, to all of which
the holder of this Certificate assents by acceptance hereof.

CHANCELLOR MEDIA CORPORATION IS AUTHORIZED TO ISSUE SHARES OF MORE THAN ONE
CLASS AND/OR TO ISSUE SHARES IN MORE THAN ONE SERIES OF AT LEAST ONE CLASS.
CHANCELLOR MEDIA CORPORATION WILL FURNISH WITHOUT CHARGE TO EACH STOCKHOLDER
WHO SO REQUESTS A STATEMENT OF THE POWERS, DESIGNATIONS, PREFERENCES AND
RELATIVE, PARTICIPATING, OPTIONAL OR OTHER SPECIAL RIGHTS OF EACH CLASS OF
STOCK OR SERIES THEREOF AND THE QUALIFICATIONS, LIMITATIONS OR RESTRICTIONS OF
SUCH PREFERENCES AND/OR RIGHTS.

THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO RESTRICTIONS
UNDER THE COMMUNICATIONS ACT OF 1934, AS AMENDED, RELATING TO OWNERSHIP BY
FOREIGN NATIONALS, FOREIGN ENTITIES, FOREIGN GOVERNMENTS OR REPRESENTATIVES OF
THE FOREGOING.

--------------------------------------------------------------------------------

    The following abbreviations, when used in the inscription on the face of 
this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:

 TEN COM - as tenants in common      UNIF GIFT MIN ACT -      Custodian
 TEN ENT - as tenants by the                            ------         --------
           entireties                                   (Cust)          (Minor)
 JT TEN -  as joint tenants with                        under Uniform Gifts to
           right of survivorship                        Minors
           and not as tenants                           Act
           in common                                       ------------------
                                                              (State)


   Additional abbreviations may also be used though not in the above list.


        For Value received,         hereby sell, assign and transfer unto 
                            --------

  PLEASE INSERT SOCIAL SECURITY OR OTHER
      IDENTIFYING NUMBER OF ASSIGNEE
  [                                    ]
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  ----------------------------------------------------------------------------
           (PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS OF ASSIGNEE)

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                                                                        Shares
  ----------------------------------------------------------------------
  of the preferred stock represented by the within Certificate, and do hereby
  irrevocably constitute and appoint
                                                                      Attorney
  --------------------------------------------------------------------
  to transfer the said shares on the books of the within-named Corporation 
  with full power of substitution in the premises.

                          
                          
  Dated,                          X 
        ------------------         -------------------------------------------

                                  X 
                                   -------------------------------------------
                                   NOTICE: THE SIGNATURE(S) TO THIS ASSIGNMENT
                                   MUST CORRESPOND WITH THE NAME(S) AS WRITTEN
                                   UPON THE FACE OF THE CERTIFICATE IN EVERY 
                                   PARTICULAR, WITHOUT ALTERATION OR 
                                   ENLARGEMENT, OR ANY CHANGE WHATEVER.



          SIGNATURE(S) GUARANTEED:
                                   -------------------------------------------
                                   NOTICE: SIGNATURE(S) SHOULD BE GUARANTEED BY
                                   A QUALIFIED MEDALLION GUARANTEE MEMBER AND 
                                   MUST CORRESPOND EXACTLY WITH THE NAME AS 
                                   WRITTEN UPON THE FACE OF THE CERTIFICATE.

        
