<PAGE>   1
                                                                     Exhibit 4.7

                               FIRST AMENDMENT TO
                        STERLING CHEMICALS HOLDINGS, INC.
                             STOCKHOLDERS AGREEMENT

              THIS FIRST AMENDMENT TO STERLING CHEMICALS HOLDINGS, INC.
STOCKHOLDERS AGREEMENT (this "Amendment") dated effective as of December 31,
1997 is by and among STERLING CHEMICALS HOLDINGS, INC., a Delaware corporation
(the "Corporation"), STERLING CHEMICALS, INC. EMPLOYEE STOCK OWNERSHIP TRUST, an
employee stock ownership trust created pursuant to the Sterling Chemicals, Inc.,
Employee Stock Ownership Plan (the "ESOT"), and the other persons and entities
whose signatures appear on the signature pages hereof (the "Other Parties" and,
together with the Corporation and the ESOT, the "Parties"). Capitalized terms
used but not defined herein shall have the respective meanings ascribed to such
terms in the Original Agreement referred to below.

                             PRELIMINARY STATEMENTS

       1.     The Parties, together with certain other Holders, are parties to
              that certain Sterling Chemicals Holdings, Inc. Stockholders
              Agreement dated effective as of August 21, 1996 (the "Original
              Agreement").

       2.     The Parties desire to amend the Original Agreement in certain
              respects in order to, among other things, permit the Holders under
              certain circumstances to transfer certain of their shares of Stock
              by way of gift without first offering such shares of Stock to the
              Corporation, the ESOT or the other Holders.

              NOW, THEREFORE, in consideration of the premises and the mutual
covenants contained herein and in the Original Agreement, and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto, intending to be legally bound, hereby agree as
follows:

              Section 1. Amendment of Section 4.6 of the Original Agreement. The
last sentence of Section 4.6 of the Original Agreement is hereby amended to read
in its entirety as follows:

       The Purchase Price of any Shares Subject to the Offer purchased by any
       Eligible Offeree under Sections 3.2 through 3.5 shall be paid in the form
       of a cashier's check or such other form of consideration mutually
       acceptable to the party making the Acquisition Proposal and the
       purchasing Eligible Offerees.

              Section 2. Amendment of Section 5.2(b) of the Original Agreement.
Section 5.2(b) of the Original Agreement is hereby amended by replacing the
phrase "at the election of the Control Offeror" appearing in clause (2) thereof
with the phrase "at the election of the Control Offeree".


<PAGE>   2

              Section 3. Amendment of Section 6 of the Original Agreement.
Section 6 of the Original Agreement is hereby amended by inserting the word
"and" at the end of subsection 6.19 thereof and adding a new subsection 6.20 to
read in its entirety as follows:

              6.20. by any Holder to any person or entity as a gift; provided,
       however, that the aggregate number of shares of Stock that may be
       transferred by any Holder pursuant to this subsection 6.20 during any
       calendar year may not exceed 20,000 (as such number may be adjusted from
       time to time to reflect any stock split, combination of shares,
       recapitalization or other similar event);

              Section 4. Amendment of Section 13.11 of the Original Agreement.
Section 13.11 of the Original Agreement is hereby amended to read in its
entirety as follows:

              13.11. Enforceability. This Agreement shall be enforceable by and
       against the Company, the Holders, the ESOT and their respective spouses,
       guardians, heirs, legatees, executors, legal representatives,
       administrators, and permitted successors and assignees.

              Section 5. Effect of Amendments. Except as amended and modified by
this Amendment, the Original Agreement shall continue in full force and effect.
The Original Agreement and this Amendment shall be read, taken and construed as
one and the same instrument. Upon the effectiveness of this Amendment, each
reference in the Original Agreement to "this Agreement" shall mean and be a
reference to the Original Agreement as amended hereby.

              Section 6. Effectiveness. This Amendment shall not be or become
effective unless and until it has been duly executed and delivered by the
Corporation and Holders constituting a Required Voting Percentage.

              Section 7. Binding Effect. This Amendment shall inure to the
benefit of, and shall be binding upon (i) the Corporation and its successors and
permitted assigns and (ii) the Holders and their respective heirs, legatees,
executors, personal representatives, administrators, successors and permitted
assigns.

              Section 8. Counterparts. This Amendment may be executed in two or
more counterparts, each of which shall be deemed an original but all of which
taken together shall constitute one and the same agreement. It shall not be
necessary in making proof of this Amendment to produce or account for more than
one such counterpart.

              Section 9. Severability. Should any clause, sentence, paragraph,
subsection or Section of this Amendment be judicially declared to be invalid,
unenforceable or void, such decision will not have the effect of invalidating or
voiding the remainder of this Amendment, and the Parties agree that the part or
parts of this Amendment so held to be invalid, unenforceable or void will be
deemed to have been stricken herefrom as if such stricken part or parts had
never been included herein.


                                      -2-
<PAGE>   3

              Section 10. Governing Law. THIS AMENDMENT SHALL BE CONSTRUED AND
ENFORCED IN ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY,
THE INTERNAL LAWS OF THE STATE OF DELAWARE, WITHOUT REFERENCE TO PRINCIPLES OF
CONFLICTS OF LAW.

              Section 11. Entire Agreement. This Amendment and the Original
Agreement set forth all of the promises, agreements, conditions, understandings,
warranties and representations among the Parties with respect to the matters
cover hereby, and supersede all prior agreements, arrangements and
understandings among the Parties, whether written, oral or otherwise. There are
no promises, agreements, conditions, understandings, warranties or
representations, oral or written, express or implied, among the Parties
concerning the subject matter hereof or thereof except as set forth herein or
therein.

              IN WITNESS WHEREOF, the Parties have executed this Amendment
effective as of the date first written above.


                                      STERLING CHEMICALS HOLDINGS, INC.



                                      By: /s/ DAVID G. ELKINS
                                         ---------------------------------------
                                      Printed Name: David G. Elkins
                                                   -----------------------------
                                      Title: Vice President
                                             -----------------------------------

                                      STERLING CHEMICALS, INC.
                                      EMPLOYEE STOCK OWNERSHIP TRUST

                                      By:  Merrill Lynch, Pierce, Fenner & Smith
                                           Incorporated, solely in its capacity 
                                           as Trustee



                                           By:
                                              ----------------------------------
                                           Printed Name:
                                                         -----------------------
                                           Title:
                                                   -----------------------------



                                      -3-
<PAGE>   4



                                        OTHER PARTIES:


                                        Individual:


                                        /s/ LAURA M. NEUMAN
                                        ----------------------------------------
                                        Printed Name: Laura M. Neuman
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                                --------------------------------



                                      -4-
<PAGE>   5

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ WILLIAM E. STREETMAN
                                        ----------------------------------------
                                        Printed Name: William E. Streetman
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-
<PAGE>   6

                                        OTHER PARTIES:


                                        Individual:


                                        
                                        ----------------------------------------
                                        Printed Name:
                                                     ---------------------------

                                        Entity:

                                        Clipper Capital Associates, Inc.
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By: /s/ EUGENE P. LYNCH
                                            ------------------------------------
                                        Printed Name: Eugene P. Lynch
                                                     ---------------------------
                                        Title: Treasurer & Secretary
                                               ---------------------------------



                                      -4-
<PAGE>   7

                                        OTHER PARTIES:


                                        Individual:


          
                                        ----------------------------------------
                                        Printed Name:
                                                     ---------------------------

                                        Entity:

                                        Chase Equity Associates, L.P.
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By: /s/ GEORGE E. KEITS III
                                            ------------------------------------
                                        Printed Name: George E. Keits III
                                                     ---------------------------
                                        Title: Managing Director and Chief
                                               ---------------------------------
                                               Administrative Officer of Chase
                                               ---------------------------------
                                               Capital Partners, General 
                                               ---------------------------------
                                               Partner
                                               ---------------------------------



                                      -4-
<PAGE>   8

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ J.R. BALL Trustee
                                        ----------------------------------------
                                        Printed Name: J.R. Ball  IRA
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-
<PAGE>   9

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ RAYMOND McLAUGHLIN
                                        ----------------------------------------
                                        Printed Name: Raymond McLaughlin
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-
<PAGE>   10





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ [ILLEGIBLE]
                                        ----------------------------------------
                                        Printed Name:   [ILLEGIBLE]           
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   11





                                        OTHER PARTIES:


                                        Individual:




                                        ----------------------------------------
                                        Printed Name: 
                                                     ---------------------------
                                        Entity:

                                        The CIT Group/Equity Investments, Inc.
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By: /s/ COLBY W. COLLINS
                                           -------------------------------------
                                        Printed Name: Colby W. Collins
                                                     ---------------------------
                                        Title:  Managing Director
                                              ----------------------------------







                                      -4-
<PAGE>   12





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ FRANK A. VANDIVER
                                        ----------------------------------------
                                        Printed Name:   Frank A. Vandiver     
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   13





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ JOHN K. O'CONNOR
                                        ----------------------------------------
                                        Printed Name:   John K. O'Connor      
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------







                                      -4-
<PAGE>   14





                                        OTHER PARTIES:


                                        Individual:




                                        ----------------------------------------
                                        Printed Name:   
                                                     ---------------------------
                                        Entity:

                                        The Rheney Living Trust
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:  /s/ SUSAN O. RHENEY              
                                           -------------------------------------
                                        Printed Name:  Susan O. Rheney        
                                                     ---------------------------
                                        Title:  Trustee                      
                                              ----------------------------------















                                      -4-
<PAGE>   15





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ ALFRED C. GLASSELL, JR.
                                        ----------------------------------------
                                        Printed Name:   Alfred C. Glassell, Jr.
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   16





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ ALLAN R. DRAGONE
                                        ----------------------------------------
                                        Printed Name:   Allan R. Dragone      
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   17





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ SCOTT A. LAWIT
                                        ----------------------------------------
                                        Printed Name:  Scott A. Lawit
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   18





                                        OTHER PARTIES:


                                        Individual:



                                        /s/  JOHN D. HAWKINS
                                        ----------------------------------------
                                        Printed Name:  John D. Hawkins
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   19





                                        OTHER PARTIES:


                                        Individual:



                                        /s/  JOSEPH A. BAJ
                                        ----------------------------------------
                                        Printed Name:  Joseph A. Baj
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   20

                                        OTHER PARTIES:


                                        Individual:



                                        ----------------------------------------
                                        Printed Name:
                                                     ---------------------------

                                        Entity:

                                        Vanderbilt University
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By: /s/ GEORGE B. STADLER
                                            ------------------------------------
                                        Printed Name: George B. Stadler
                                                     ---------------------------
                                        Title: Assistant Treasurer
                                               ---------------------------------



                                      -4-
<PAGE>   21

                                        OTHER PARTIES:


                                        Individual:


                                        
                                        ----------------------------------------
                                        Printed Name:
                                                     ---------------------------

                                        Entity:

                                        The Baylor School
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By: /s/ HUGH W. HUDDLESTON
                                            ------------------------------------
                                        Printed Name: Hugh W. Huddleston
                                                     ---------------------------
                                        Title: Treasurer 3/2/98
                                               ---------------------------------



                                      -4-
<PAGE>   22

<TABLE>

<S>                                                       <C>
                                                          OTHER PARTIES:


                                                          Individual:


                                                          /s/ MINDY LANIGAN
                                                          -----------------------------------
Investor:             Chartwell Capital Investors, L.P.   Printed Name: Mindy Lanigan
                                                                        ---------------------
Its General Partner:  Chartwell Capital Partners, L.P.
                                                          Entity:
Its General Partner:  Chartwell Partners, L.P.
                                                          -----------------------------------
Its General Partner:  Chartwell, Inc.                     (Print Name of Entity)



                                                          By:
                                                             --------------------------------
                                                          Printed Name:
                                                                        ---------------------
                                                          Title:
                                                                 ----------------------------

</TABLE>

                                      -4-
<PAGE>   23

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ SAMUEL Z. CHAMBERLAIN
                                        ----------------------------------------
                                        Printed Name: Samuel Z. Chamberlain
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-
<PAGE>   24

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ DAVID HEANEY
                                        ----------------------------------------
                                        Printed Name:  David Heaney
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-




<PAGE>   25

                                        OTHER PARTIES:


                                        Individual:


                                        /s/ DAVID G. ELKINS     
                                        ----------------------------------------
                                        Printed Name:  David G. Elkins
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-


<PAGE>   26


                                        OTHER PARTIES:


                                        Individual: 

                                        /s/ MICHAEL G. MARK      
                                            DORIS M. MARK
                                        ----------------------------------------
                                        Printed Name:  Michael G. Mark
                                                       Doris M. Mark
                                                     ---------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



                                      -4-

<PAGE>   27

                                        OTHER PARTIES:


                                        Individual: 
                                                    
                                        /s/  RAY W. GRIFFIN, III BY
                                             MARIAN OEHMIG LATIMER, POA
                                        ----------------------------------------
                                        Printed Name:  Ray W. Griffin III by
                                                     ---------------------------
                                         Marian Oehmig Latimer
                                        ----------------------------------------

                                        Entity:

                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:
                                            ------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Title:
                                               ---------------------------------



Address correction:


          8 Bartram Road
          Lookout Mountain, TN 37350



                                      -4-


<PAGE>   28





                                        OTHER PARTIES:


                                        Individual:



                                        /s/  MARIAN OEHMIG LATIMER
                                        ----------------------------------------
                                        Printed Name:  Marian Oehmig Latimer
                                                       -------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------

Address Correction:
     8 Bartram Road
     Lookout Mountain, TN 37350



                                      -4-
<PAGE>   29





                                        OTHER PARTIES:


                                        Individual:



                                        
                                        ----------------------------------------
                                        Printed Name:
                                                      --------------------------
                                        Entity:

                                        Kinkaid Investments Foundation
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:  /s/ JOANNE WILSON
                                           -------------------------------------
                                        Printed Name:  Joanne Wilson          
                                                     ---------------------------
                                        Title:   Assistant Treasurer         
                                              ----------------------------------





                                      -4-
<PAGE>   30





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ MARK DAVIS
                                        ----------------------------------------
                                        Printed Name:  Mark Davis
                                                       -------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   31





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ [ILLEGIBLE]
                                        ----------------------------------------
                                        Printed Name:  [ILLEGIBLE]
                                                       -------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   32





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ MICHAEL J. A. LOBO
                                        ----------------------------------------
                                        Printed Name:  Michael J. A. Lobo

                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   33





                                        OTHER PARTIES:


                                        Individual:



                                        /s/  [ILLEGIBLE]
                                        ----------------------------------------
                                        Printed Name:  
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-
<PAGE>   34





                                        OTHER PARTIES:


                                        Individual:



                                        /s/
                                        ----------------------------------------
                                        Printed Name:
                                                     ---------------------------
                                        Entity:

                                        Koch Capital Services, Inc.
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:   /s/ JOHN C. PITTENGER
                                           -------------------------------------
                                        Printed Name:  John C. Pittenger      
                                                     ---------------------------
                                        Title:    Vice President             
                                              ----------------------------------





                                      -4-
<PAGE>   35





                                        OTHER PARTIES:


                                        Individual:



                                        /s/ FRANK J. HENRDEJS
                                        ----------------------------------------
                                        Printed Name:  Frank J. Henrdejs
                                                     ---------------------------
                                        Entity:

                                        
                                        ----------------------------------------
                                        (Print Name of Entity)



                                        By:                                   
                                           -------------------------------------
                                        Printed Name:                         
                                                     ---------------------------
                                        Title:                               
                                              ----------------------------------





                                      -4-