Document:

<PAGE>   1
                                                                  EXHIBIT 4.10.4

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

                               AMFM OPERATING INC.

                                   AS OBLIGOR

                                       AND

                           THE GUARANTORS NAMED HEREIN

                                       AND

                              THE BANK OF NEW YORK,

                                   AS TRUSTEE

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

                          THIRD SUPPLEMENTAL INDENTURE

                          DATED AS OF JANUARY 18, 2000

                                       TO

                                    INDENTURE

                          DATED AS OF DECEMBER 22, 1997

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

                                  $500,000,000

                   8 1/8% SENIOR SUBORDINATED NOTES DUE 2007

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

<PAGE>   2

         THIRD SUPPLEMENTAL INDENTURE dated as of January 18, 2000, among AMFM
OPERATING INC., a Delaware corporation (the "Company"), the subsidiaries listed
on Schedule I hereto (collectively, the "New Subsidiary Guarantors") and THE
BANK OF NEW YORK, a New York banking corporation, as Trustee (the "Trustee").

         WHEREAS, Chancellor Media Corporation of Los Angeles, a Delaware
corporation "CMCLA") and certain subsidiary guarantors have heretofore executed
and delivered to the Trustee an Indenture dated as of December 22, 1997, as
amended by that certain First Supplemental Indenture dated as of August 23, 1999
by and among CMCLA, the guarantors named therein and the Trustee and that
certain Second Supplemental Indenture dated as of November 19, 1999 by and among
the Company, the guarantors named therein and the Trustee (as amended, the
"Indenture"), providing for the issuance of $500,000,000 aggregate principal
amount of 8 1/8% Senior Subordinated Notes due 2007 (the "Notes");

         WHEREAS, pursuant to that Second Supplemental Indenture, dated as of
November 19, 1999, the Company assumed the obligations 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 4.19 and 10A.03, to add the New Subsidiary Guarantors as
guarantors.

         WHEREAS, the execution and delivery of this Third Supplemental
Indenture has been authorized by resolutions of the Boards of Directors of the
Company and each of the New Subsidiary Guarantors (and in the case of any
guarantor that is a limited partnership or a limited liability company, the
Board of Directors of the general partner or sole member, respectively); 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.

<PAGE>   3

                                   ARTICLE II

                            MISCELLANEOUS PROVISIONS

         Section 2.01 DEFINED TERMS. 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

                                       2
<PAGE>   4

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 an opinion of
Vinson & Elkins L.L.P., counsel to the Company, which shall be dated no earlier
than the date hereof.

            [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

                                       3
<PAGE>   5

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

                          AMFM OPERATING INC.,
                          as Obligor

                          By: /s/ W. Schuyler Hansen
                              --------------------------------------------------
                              W. Schuyler Hansen
                              Senior Vice President and Chief Accounting Officer

                          ON BEHALF OF EACH OF THE NEW SUBSIDIARY
                          GUARANTORS LISTED ON SCHEDULE I HERETO*

                          By: /s/ Kathy Archer
                              --------------------------------------------------
                              Kathy Archer
                              Senior Vice President

                          THE BANK OF NEW YORK,
                          as Trustee

                          /s/ Remo J. Reale
                          ------------------------------------------------------
                          By: Remo J. Reale
                              --------------------------------------------------
                          Title: Vice President
                                 -----------------------------------------------

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

*For AMFM LA, LLC, by the Company, its sole member. For AMFM Texas, LLC, by
Chancellor Media/Shamrock Broadcasting, Inc., its sole member.

<PAGE>   6

                                   SCHEDULE I

                            NEW SUBSIDIARY GUARANTORS

AMFM San Diego, Inc., a Delaware corporation
AMFM Washington D.C., Inc., a Delaware corporation
AMFM LA, LLC, a Delaware limited liability company
AMFM Texas, LLC, a Delaware limited liability company<PAGE>   1
                                                                  EXHIBIT 4.11.2

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

                   CHANCELLOR MEDIA CORPORATION OF LOS ANGELES

                                   as Obligor

                                       AND

                           the Guarantors named herein

                                       AND

                              THE BANK OF NEW YORK,

                                   as Trustee

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

                          FIRST SUPPLEMENTAL INDENTURE

                           Dated as of August 23, 1999

                                       to

                                    Indenture

                         Dated as of September 30, 1998

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

                                  $750,000,000

                          9% Senior Subordinated Notes

                               due October 1, 2008

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

<PAGE>   2

         FIRST 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 THE BANK OF NEW YORK, a New York banking
corporation, as Trustee (the "Trustee").

         WHEREAS, the Company and certain subsidiary guarantors have heretofore
executed and delivered to the Trustee an Indenture dated as of September 30,
1998 (the "Indenture"), providing for the issuance of $750,000,000 aggregate
principal amount of 9% Senior Subordinated Notes due October 1, 2008 (the
"Notes"); and

         WHEREAS, the Company, the New Subsidiary Guarantors and the Trustee
desire by this First Supplemental Indenture pursuant to and as contemplated by
the provisions of the Indenture relating to the addition of guarantors,
including Sections 4.19, 9.01 and 11.03, to add the New Subsidiary Guarantors as
guarantors pursuant to the terms of the Indenture; and

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

         WHEREAS, all conditions and requirements necessary to make this First
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 First 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 First Supplemental Indenture.

                                   ARTICLE II.

                            MISCELLANEOUS PROVISIONS

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

                                       2
<PAGE>   3

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 FIRST 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 First Supplemental Indenture and the Notes shall bind their
successors. All agreements of the Trustee in this First Supplemental Indenture
shall bind its successors.

Section 2.05. Duplicate Originals. All parties may sign any number of copies of
this First 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
First 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 First 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 First
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 First 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.

            (THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK)

                                       3
<PAGE>   4

         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/
        -------------------------

                                         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/
        -------------------------

                                         THE BANK OF NEW YORK,
                                         as Trustee

                                         /s/ Remo J. Reale
                                         ---------------------------------------
                                         By:      Remo J. Reale
                                         Title:   Vice President

Attest: /s/
        -------------------------

                                       4
<PAGE>   5
                                   SCHEDULE I

                            NEW SUBSIDIARY GUARANTORS

Chancellor Media Corporation of Ohio (a Delaware corporation)
Cleveland Radio Licenses, LLC (a Delaware limited liability company)
Hardin Development Corporation (a Florida corporation)
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)
Zebra Broadcasting Corporation (an Ohio corporation)

                                       5

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00003-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00003-of-00352.parquet"}]]