<PAGE>   1
                                                                   EXHIBIT 4.9.3


================================================================================


                   CHANCELLOR MEDIA CORPORATION OF LOS ANGELES


                                   as Obligor


                                       AND


                           the Guarantors named herein


                                       AND


                     AMERICAN STOCK TRANSFER & TRUST COMPANY


                                   as Trustee

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


                          THIRD SUPPLEMENTAL INDENTURE



                           Dated as of August 23, 1999


                                       to


                                    Indenture

                          Dated as of December 19, 1996


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

                                  $100,000,000

                        10-1/2% Senior Subordinated Notes

                                    due 2007


================================================================================


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         THIRD SUPPLEMENTAL INDENTURE dated as of August 23, 1999, among
CHANCELLOR MEDIA CORPORATION OF LOS ANGELES, a Delaware corporation (the
"Company"), the subsidiaries listed on Schedule I hereto (collectively, the "New
Subsidiary Guarantors") and AMERICAN STOCK TRANSFER & TRUST COMPANY, a New York
banking association, as Trustee (the "Trustee").

         WHEREAS, Katz Media Corporation ("Katz Media") and the subsidiary
guarantors named therein have heretofore executed and delivered to the Trustee
an Indenture dated as of December 19, 1996, as amended and restated pursuant to
the First Supplemental Indenture among Katz Media, the subsidiary guarantors
named therein and the Trustee dated as of October 28, 1997, and amended by the
Second Supplemental Indenture, dated as of October 28, 1997, by and among the
Company, the subsidiary guarantors named therein and the Trustee (as amended and
restated, the "Indenture"), providing for the issuance of $100,000,000 aggregate
principal amount of Katz Media's 10-1/2% Senior Subordinated Notes due 2007 (the
"Notes");

         WHEREAS, pursuant to that certain Agreement and Plan of Merger by and
between the Company and Katz Media dated as of October 28, 1997 (the "Merger
Agreement"), Katz Media merged with and into the Company (the "Merger");

         WHEREAS, pursuant to that Second Supplemental Indenture dated as of
October 28, 1997, the Company assumed the obligations of Katz Media under the
Notes and the Indenture;

         WHEREAS, the Company, the New Subsidiary Guarantors and the Trustee
desire by this Third Supplemental Indenture, pursuant to and as contemplated by
the provisions of the Indenture relating to the addition of guarantors,
including Sections 4.15, 9.01 and 11.05, to add the New Subsidiary Guarantors as
guarantors thereunder;

         WHEREAS, the execution and delivery of this Third Supplemental
Indenture has been authorized by resolutions of the Boards of Directors of the
Company and the New Subsidiary Guarantors; and

         WHEREAS, all conditions and requirements necessary to make this Third
Supplemental Indenture a valid, binding legal instrument in accordance with its
terms have been performed and fulfilled by the parties hereto and the execution
and delivery thereof have been in all respects duly authorized by the parties
hereto.

         NOW, THEREFORE, in consideration of the above premises, each party
agrees, for the benefit of the others and for the equal and ratable benefit of
the holders of the Notes, as follows:

                                   ARTICLE I.
                     ASSUMPTION OF OBLIGATIONS AS GUARANTOR

Section 1.01. Assumption. Each of the New Subsidiary Guarantors hereby expressly
and unconditionally assumes each and every covenant, agreement and undertaking
of a Guarantor in the Indenture as of the date of this Third Supplemental
Indenture, and also hereby expressly and unconditionally assumes each and every
covenant, agreement and undertaking of a Guarantor in each Note outstanding on
the date of this Third Supplemental Indenture.



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                                   ARTICLE II.
                            MISCELLANEOUS PROVISIONS

Section 2.01. Terms Defined. For all purposes of this Third Supplemental
Indenture, except as otherwise defined or unless the context otherwise requires,
terms used in capitalized form in this Third Supplemental Indenture and defined
in the Indenture have the meanings specified in the Indenture.

Section 2.02. Indenture. Except as amended hereby, the Indenture and the Notes
are in all respects ratified and confirmed and all the terms shall remain in
full force and effect.

Section 2.03. Governing Law. This Third Supplemental Indenture shall be governed
by and construed in accordance with the laws of the State of New York, as
applied to contracts made and performed within the State of New York, without
regard to principles of conflict of laws.

Section 2.04. Successors. All agreements of the Company and the New Subsidiary
Guarantors in this Third Supplemental Indenture and the Notes shall bind their
successors. All agreements of the Trustee in this Third Supplemental Indenture
shall bind its successors.

Section 2.05. Duplicate Originals. All parties may sign any number of copies of
this Third Supplemental Indenture. Each signed copy shall be an original, but
all of them together shall represent the same agreement.

Section 2.06. Severability. In case any one or more of the provisions in this
Third Supplemental Indenture or in the Notes shall be held invalid, illegal or
unenforceable, in any respect for any reason, the validity, legality and
enforceability of any such provision in every other respect and of the remaining
provisions shall not in any way be affected or impaired thereby, it being
intended that all of the provisions hereof shall be enforceable to the full
extent permitted by law.

Section 2.07. Trustee Disclaimer. The Trustee accepts the amendment of the
Indenture effected by this Third Supplemental Indenture and agrees to execute
the trust created by the Indenture as hereby amended, but on the terms and
conditions set forth in the Indenture, including the terms and provisions
defining and limiting the liabilities and responsibilities of the Trustee, which
terms and provisions shall in like manner define and limit its liabilities and
responsibilities in the performance of the trust created by the Indenture as
hereby amended, and without limiting the generality of the foregoing, the
Trustee shall not be responsible in any manner whatsoever for or with respect to
any of the recitals or statements contained herein, all of which recitals or
statements are made solely by the Company and the New Subsidiary Guarantors, or
for or with respect to (i) the validity or sufficiency of this Third
Supplemental Indenture or any of the terms or provisions hereof, (ii) the proper
authorization hereof by the Company and the New Subsidiary Guarantors by
corporate action or otherwise, (iii) the due execution hereof by the Company and
the New Subsidiary Guarantors or (iv) the consequences (direct or indirect and
whether deliberate or inadvertent) of any amendment herein provided for, and the
Trustee makes no representation with respect to any such matters.

Section 2.08. Effectiveness. This Third Supplemental Indenture shall become
effective, once executed, upon receipt by the Trustee of a certificate of an
appropriate officer of the Company; and an opinion of Weil, Gotshal & Manges
LLP, counsel to the Company, each of which shall be dated no earlier than the
date hereof.



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         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the day and year written above.




                                         CHANCELLOR MEDIA CORPORATION OF LOS
                                         ANGELES, as Obligor

                                         /s/ William S. Banowsky, Jr.
                                         ---------------------------------------
                                         By:      William S. Banowsky, Jr.
                                         Title:   Executive Vice President

Attest:   /s/ Susan McGiffert
       ----------------------------


                                         On Behalf of Each of the New Subsidiary
                                         Guarantors Listed on Schedule I hereto


                                         /s/ William S. Banowsky, Jr.
                                         ---------------------------------------
                                         By:      William S. Banowsky, Jr.
                                         Title:   Executive Vice President

Attest:   /s/ Susan McGiffert
       ----------------------------

                                         AMERICAN STOCK TRANSFER & TRUST COMPANY
                                         as Trustee

                                         /s/ Herbert J. Lemmer
                                         ---------------------------------------
                                         By:      Herbert J. Lemmer
                                         Title:   Vice President

Attest:   /s/ Susan Sidler
       ----------------------------



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                                   SCHEDULE I

                            NEW SUBSIDIARY GUARANTORS
            (ALL NEW SUBSIDIARY GUARANTORS ARE DELAWARE CORPORATIONS
                         EXCEPT AS EXPRESSLY INDICATED)


The AMFM Radio Networks, Inc.
Chancellor Media Air Services Corporation
Chancellor Media Corporation of Michigan
Chancellor Media Corporation of New York
Chancellor Media Corporation of Ohio
Chancellor Media Martin Corporation
Chancellor Media MW Sign Corporation
Chancellor Media Nevada Sign Corporation
Chancellor Media Outdoor Corporation
Chancellor Media Radio Licenses, LLC (a Delaware limited liability company)
Chancellor Media/ Shamrock Radio Licenses, LLC (a Delaware limited liability
     company)
Chancellor Media Whiteco Outdoor Corporation Cleveland Radio Licenses, LLC (a
     Delaware limited liability company)
Dowling Company Incorporated (a Virginia corporation)
Hardin Development Corporation (a Florida corporation)
Martin Media, L.P. (a California limited partnership)
Outdoor Promotions West, LLC (a Delaware limited liability company)
Parsons Development Company (a Florida corporation)
Revolution Outdoor Advertising, Inc. (a Florida corporation)
Transit America Las Vegas, LLC (a Delaware limited liability company)
Triumph Outdoor Holdings, LLC (a Delaware limited liability company)
Triumph Outdoor Louisiana, LLC (a Delaware limited liability company)
Triumph Outdoor Rhode Island, LLC (a Delaware limited liability company)
Western Poster Service, Inc. (a Texas corporation)
Zebra Broadcasting Corporation (an Ohio corporation)



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