<PAGE>   1
 
                                                                    EXHIBIT 12.1
 
                  CHANCELLOR MEDIA CORPORATION OF LOS ANGELES
 
               COMPUTATION OF RATIO OF EARNINGS TO FIXED CHARGES
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                                  ACTUAL     ACTUAL
                                                                                   SIX         SIX       PRO FORMA     PRO FORMA
                                                                                  MONTHS     MONTHS         YEAR       SIX MONTHS
                                          YEAR ENDED DECEMBER 31,                 ENDED       ENDED        ENDED         ENDED
                             -------------------------------------------------   JUNE 30,   JUNE 30,    DECEMBER 31,    JUNE 30,
                               1993      1994      1995       1996      1997       1997       1998          1997          1998
                             --------   -------   -------   --------   -------   --------   ---------   ------------   ----------
<S>                          <C>        <C>       <C>       <C>        <C>       <C>        <C>         <C>            <C>
Earnings:
  Net income (loss) before
    income taxes...........  $(20,749)  $    39   $(5,658)  $(19,090)  $(6,692)  $ 8,118    $(101,465)   $(354,666)    $(207,885)
  Fixed charges............    15,086    15,252    20,854     40,461    89,325    24,413       96,640      382,287       191,304
                             --------   -------   -------   --------   -------   -------    ---------    ---------     ---------
  Earnings as
    adjusted(A)............  $ (5,663)  $15,291   $15,196   $ 21,371   $82,633   $32,531    $  (4,825)   $  27,621     $ (16,581)
                             ========   =======   =======   ========   =======   =======    =========    =========     =========
Fixed Charges:
  Interest expense.........  $ 13,878   $13,809   $19,199   $ 37,527   $85,017   $22,741    $  92,358    $ 371,516     $ 185,758
  Amortization of deferred
    financing costs........       728       712       631      1,113     1,337       590        1,438        4,875         2,438
  Rents under leases
    representative of an
    interest factor(1).....       480       731     1,024      1,821     2,971     1,082        2,844        5,896         3,108
                             --------   -------   -------   --------   -------   -------    ---------    ---------     ---------
Fixed charges as
  adjusted(B)..............    15,086    15,252    20,854     40,461    89,325    24,413       96,640      382,287       191,304
                             ========   =======   =======   ========   =======   =======    =========    =========     =========
Ratio of earnings to fixed
  charges (A) divided by
  (B)......................        --       1.0        --         --        --      1.33           --           --            --
Deficiency of earnings to
  fixed charges............  $ 20,749   $    --   $ 5,658   $ 19,090   $ 6,692   $    --    $ 101,465    $ 354,666     $ 207,885
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(1) Management of CMCLA believes approximately one-third of rental and lease
    expense is representative of the interest component of rent expense.