<PAGE>   1
                                                                 EXHIBIT 10.10.2

                               FIRST AMENDMENT OF
                        THE CHANCELLOR MEDIA CORPORATION
                             1999 STOCK OPTION PLAN

                  This First Amendment of the Chancellor Media Stock Option Plan
(the "Plan") is made effective as of the 13th day of July, 1999 by AMFM Inc.
(formerly known as Chancellor Media Corporation), a Delaware corporation (the
"Company").

                  WHEREAS, each of the Board of Directors of the Company and the
stockholders of the Company have heretofore adopted and approved the Plan;

                  WHEREAS, as of the date hereof, the Company has changed its
name from Chancellor Media Corporation to AMFM Inc. pursuant to that certain
merger of July 13, 1999 (the "Merger") according to the Agreement and Plan of
Merger, dated as of August 26, 1998, and amended and restated as of April 29,
1999, by and among the Company, Capstar Broadcasting Corporation, a Delaware
corporation, CBC Acquisition Company, Inc., a Delaware corporation, and CMC
Merger Sub, Inc., a Delaware corporation and a wholly-owned subsidiary of the
Company;

                  WHEREAS, the Company desires to amend the Plan to change the
vesting schedule and term of options granted thereunder; and

                  NOW, THEREFORE, the Plan is amended as follows:

                  1.  TITLE OF PLAN.

                  The title of the Plan, as set forth on the first page of the
Plan, is hereby amended to read, in its entirety, as follows:

                        AMFM INC. 1999 STOCK OPTION PLAN

                  2.  SECTION 1.

                  The name of the Company in the first sentence of Section 1 is
amended to read "AMFM Inc."

                  3.  SECTION 6(c).

                  Section 6(c) is amended in its entirety as follows:

                  "Term. The term of each Option shall be established by the
Committee and set forth at the time the Option is granted. The term of the
Option shall not exceed 3 (three) years from the date of grant of such Option;
provided, however, that Options for up to an aggregate of 500,000 shares of
Common Stock may have terms exceeding three (3) years but not exceeding ten (10)
years if the Company was contractually committed as




<PAGE>   2

of July 1, 1999 to issue such Options with such terms exceeding three (3) years.
An Option may be terminated prior to the expiration of its term in accordance
with the provisions of the Plan."

                  4.  SECTION 6(d).

                  Section 6(d) is amended in its entirety as follows:

                  "Vesting and Exercisability. Unless otherwise determined by
the Committee, and subject to the provisions of subsection 6(e), (f), (g) and
(h) below, Options granted to any Key Employee or Eligible Non-Employee pursuant
to this Section 6 shall vest and become exercisable in accordance with and on
the dates described in the schedule set forth below; provided, however, that
unless otherwise determined by the Committee, such Options shall vest and become
exercisable on any such date only if such Key Employee or Eligible non-Employee
is employed or providing services to the Company or any Related Entity on such
date:

                  o        all of the shares of Common Stock underlying such
                           Option shall vest and become exercisable on the first
                           anniversary of the date of grant of such Option.

                  No Option by its terms shall be exercisable after the
expiration of three years from the date of grant of the Option; provided,
however, that in no event shall an optionee have less than 30 days to exercise
an option which has become vested."

                  5.       SECTION 7(c).

                  "Term. The term of each Value Option shall be established by
the Committee and set forth at the time the Option is granted. The term of the
Option shall not exceed 5 (five) years from the date of grant of such Option
except as provided in subsections 7(e), (f), (g), (h), and (i). An Option may be
terminated prior to the expiration of its term in accordance with the provisions
of the Plan."

                  6.       SECTION 7(e).

                  Section 7(e) is amended in its entirety as follows (which
amendment does not amend the terms or operation of the Exercisability Value (as
such term is defined in the Plan):

"e.               Exercisability. A Value Option granted on or prior to June 1,
                  1999 shall become exercisable after the date on which the
                  average Fair Market Value of a share of Common Stock,
                  calculated on a daily basis, equals or



                                       2

<PAGE>   3



                  exceeds $100.00 per share and a Value Option granted on or
                  after June 1, 1999 shall become exercisable after the date on
                  which the Average Fair Market Value of a share of Common
                  Stock, calculated on a daily basis, equals or exceeds the
                  greater of (i) $100.00 per share or (ii) two-hundred percent
                  (200%) of the exercise price for a share of Common Stock under
                  such Option (the "Exercisability Value"), for a period of 30
                  consecutive days (excluding non-business days for the purpose)
                  during the period from (and including) the date of grant of
                  such Option through (and including) the fifth anniversary of
                  the date of grant of such Option. No Value Option (whether or
                  not vested) shall become exercisable after 5:00 p.m., in
                  Dallas, Texas, on the fifth anniversary of the date of grant
                  of such Option, and any Value Option (whether or not vested)
                  that is not exercisable at such time shall automatically, and
                  without notice, terminate and become null and void at such
                  time and any Value Option that is exercisable at such time may
                  be exercised until the 90th day after such date. In addition,
                  the exercisability of a Value Option shall be subject to
                  subsections 7(f), (g), (h) and (i) and Section 9.

                  7.       SECTION 11.

                  Section 11 is amended in its entirety as follows:

                  "Assignment or Transfer. During the lifetime of an optionee,
Options shall be exercisable only by the optionee or by the optionee's legal
representative in the event that such a representative has been appointed in
connection with the Disability of the optionee. Except as otherwise expressly
provided in any Option, no Option granted under the Plan or any rights or
interests therein shall be assignable or transferable by an optionee except by
will or the laws of descent and distribution; provided, however, that any
optionee may, subject to the approval of the Compensation Committee of the
Board, have an Option issued directly in the name of, or assign or otherwise
transfer an Option to, a trust or limited partnership established for the
benefit of such optionee's spouse, siblings, parents, children and/or
grandchildren."

                  In all other respects, the Plan is ratified and confirmed.

                                                 AMFM INC. (formerly known as
                                                 CHANCELLOR MEDIA CORPORATION)


                                                 By:   /s/
                                                       ------------------------
                                                 Name:
                                                       ------------------------
                                                 Title:
                                                       ------------------------




                                       3