<PAGE>   1
 
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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                            ------------------------
 
   
                                   FORM 10-K/A
    
                            ------------------------
 
[X]   ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF
     THE SECURITIES EXCHANGE ACT OF 1934
 
                    FOR FISCAL YEAR ENDED DECEMBER 31, 1998
                                       OR
 
[ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d) OF
     THE SECURITIES EXCHANGE ACT OF 1934
                               (NO FEE REQUIRED)
 
                        COMMISSION FILE NUMBER: 00-23473
 
                                COMBICHEM, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                       <C>
                DELAWARE                                 33-0617379
      (STATE OR OTHER JURISDICTION                    (I.R.S. EMPLOYER
    OR INCORPORATION OR ORGANIZATION)                IDENTIFICATION NO.)
          9050 CAMINO SANTA FE
       SAN DIEGO, CALIFORNIA 92121                          92121
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                 (ZIP CODE)
</TABLE>
 
              REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE:
                                  619-530-0484
 
          SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:
                                      NONE
 
          SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:
                         COMMON STOCK, PAR VALUE $0.001
 
     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]
 
   
     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K.  [ ]
    
 
     The aggregate market value of the voting stock held by nonaffiliates of the
registrant as of February 28, 1999 was approximately $28,048,947. For the
purposes of this calculation, shares owned by officers, directors and 10%
shareholders known to the registrant have been deemed to be owned by affiliates.
This determination of affiliate status is not necessarily a conclusive
determination for other purposes.
 
     The number of shares outstanding of the registrant's Common Stock as of
February 28, 1999 was 13,440,421.
 
                      DOCUMENTS INCORPORATED BY REFERENCE
 
     Portions of Registrant's Proxy Statement for the Annual Meeting of
Shareholders scheduled to be held on May 6, 1999, to be filed on or about April
6, 1999, referred to herein as the "Proxy Statement", are incorporated as
provided in Part III.
 
     Certain exhibits filed with the Registrant's prior registration statements
and Forms 10-Q are incorporated as provided in Part IV.
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                                EXPLANATORY NOTE


This Amendment No. 1 to CombiChem, Inc.'s Annual Report on Form 10-K for the 
fiscal year ended December 31, 1998 is being filed solely to reflect that the 
original filing on Form 10-K for the fiscal year ended December 31, 1998 
erroneously indicated by check mark that the disclosure of delinquent filers, 
pursuant to Item 405 of Regulation S-K, was not contained or incorporated by 
reference therein.
    
<PAGE>   3
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.
 
                                              COMBICHEM, INC.

    
Date: April 5, 1999                           By:   /s/ VICENTE ANIDO JR.
 
                                                --------------------------------
                                                    Vicente Anido Jr., Ph.D.
                                                 President and Chief Executive
                                                             Officer
 
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, this
Report has been signed below by the following persons on behalf of the
Registrant in the capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                   SIGNATURE                                TITLE                  DATE
                   ---------                                -----                  ----
<C>                                               <C>                         <S>
             /s/ VICENTE ANIDO JR.                President, Chief Executive  April 5, 1999
------------------------------------------------     Officer and Director
              Vicente Anido, Ph.D.
 
                      *                            Vice President, Finance    April 5, 1999
------------------------------------------------    and Administration and
                 Karin Eastham                     Chief Financial Officer
 
                      *                                    Director           April 5, 1999
------------------------------------------------
                 Pierre Lamond
 
                      *                                    Director           April 5, 1999
------------------------------------------------
            Philippe Chambon, Ph.D.
 
                      *                           Chief Scientific Officer,   April 5, 1999
------------------------------------------------   Chief Operating Officer
               Peter Myers, Ph.D.                        and Director
 
                      *                                    Director           April 5, 1999
------------------------------------------------
                 Arthur Reidel
 
                      *                                    Director           April 5, 1999
------------------------------------------------
              William Scott, Ph.D.
 
                      *                                    Director           April 5, 1999
------------------------------------------------
           Michael J. Pazzani, Ph.D.
</TABLE>
 

* By:   /s/ VICENTE ANIDO JR.
        --------------------------------
            Vicente Anido, Ph.D.
            Attorney-In-Fact
    

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