<PAGE>   1
                                                                    EXHIBIT 3.87

                                                                          PAGE 1

                                State of Delaware

                        Office of the Secretary of State

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


    I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY
CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF
INCORPORATION OF "CHANCELLOR MEDIA WHITECO OUTDOOR CORPORATION", FILED IN THIS
OFFICE ON THE THIRD DAY OF SEPTEMBER, A.D. 1998, AT 10:30 O'CLOCK A.M.

    A FILED COPY OF THIS CERTIFICATE HAS BEEN FORWARDED TO THE NEW CASTLE COUNTY
RECORDER OF DEEDS.







                                    /s/ Edward J. Freel
                      [STATE SEAL]  --------------------------------------------
                                    Edward J. Freel, Secretary of State


  2940835     8100                  AUTHENTICATION:  9285834

                                              DATE:  09-03-98
  981344438
<PAGE>   2
                          CERTIFICATE OF INCORPORATION

                                       OF

                  CHANCELLOR MEDIA WHITECO OUTDOOR CORPORATION


     FIRST: The name of the corporation (hereinafter sometimes referred to as
the "Corporation") is:

                  Chancellor Media Whiteco Outdoor Corporation

     SECOND: The address of the registered office of the Corporation in the
State of Delaware is 1209 Orange Street, New Castle County, Wilmington, Delaware
19801. The name of its registered agent at such address is The Corporation Trust
Company.

     THIRD: The purpose of the Corporation is to engage in any lawful act or
activity for which corporations may be organized under the General Corporation
Law of the State of Delaware.

     FOURTH: The aggregate number of all classes of shares which the Corporation
shall have authority to issue is one thousand (1,000) shares of common stock
with a par value of $.01 per share.

     No holder of shares of the Corporation of any class, now or hereafter
authorized, shall have any preferential or preemptive right to subscribe for,
purchase or receive any share of the Corporation of any class, now or hereafter
authorized, or any options or warrants for such shares, or any rights to
subscribe to or purchase such shares, or any securities convertible into or
exchangeable for such shares, which may at any time or from time to time be
issued, sold or
<PAGE>   3
offered for sale by the Corporation; provided, however, that in connection with
the issuance or sale of any such shares or securities, the Board of Directors of
the Corporation may, in its sole discretion, offer such shares or securities, or
any part thereof, for purchase or subscription by the holders of shares of the
Corporation, except as may otherwise be provided by this Certificate of
Incorporation as from time to time amended.

     At all times, each holder of common stock of the Corporation shall be
entitled to one vote for each share of common stock held by such stockholder
standing in the name of such stockholder on the books of the Corporation.

     FIFTH: The name and address of the Incorporator is as follows:

                         Nancy J. Mellady
                         LATHAM & WATKINS
                         1001 Pennsylvania Avenue, Suite 1300
                         Washington, D.C. 20004-2505

     SIXTH: In furtherance and not in limitation of the powers conferred by
statute, the Board of Directors is expressly authorized to make, alter or repeal
the Bylaws of the Corporation.

     SEVENTH: No director of the Corporation shall be liable to the Corporation
or its stockholders for monetary damages for the breach of fiduciary duty as a
director, except for liability (i) for any breach of the director's duty of
loyalty to the Corporation or its stockholders, (ii) for acts or omissions not
in good faith or which involved intentional misconduct or a knowing violation of
law, (iii) under Section 174 of the Delaware General Corporation Law, or (iv)
for any transaction from which the director derived an improper personal
benefit.

     EIGHTH: Election of directors need not be by written ballot unless the
Bylaws of the Corporation shall so provide.
<PAGE>   4
     NINTH: The Corporation reserves the right to amend, alter, change or repeal
any provisions contained in this Certificate of Incorporation, in the manner now
or hereafter prescribed by the law of the State of Delaware. All rights
conferred upon stockholders herein are granted subject to this reservation.
<PAGE>   5
     I, THE UNDERSIGNED, being the sole incorporator hereinbefore named, for the
purpose of forming a corporation pursuant to the General Corporation Law of the
State of Delaware, do make this certificate, herein declaring and certifying
that this is my act and deed and the facts herein stated are true, and
accordingly have hereunto set my hand this 3rd day of September, 1998.




                                   /s/  Nancy J. Mellady
                                   -------------------------------------
                                   Nancy J. Mellady
                                   Incorporator