<PAGE>   1
                                                                EXHIBIT 4.20(a)

                               FIRST AMENDMENT TO
                           REVOLVING CREDIT AGREEMENT

              THIS FIRST AMENDMENT TO REVOLVING CREDIT AGREEMENT (this
"Amendment") dated as of the Amendment Effective Date (as defined in Section 4
of this Amendment) is by and among STERLING CHEMICALS, INC., a Delaware
corporation ("Sterling"), STERLING CANADA, INC., a Delaware corporation,
STERLING CHEMICALS ENERGY, INC., a Delaware corporation, STERLING CHEMICALS
INTERNATIONAL, INC., a Delaware corporation, STERLING FIBERS, INC., a Delaware
corporation, STERLING PULP CHEMICALS, INC., a Georgia corporation, and STERLING
PULP CHEMICALS US, INC., a Delaware corporation (each such entity, together
with Sterling, each individually a "Borrower" and collectively the
"Borrowers"), THE CIT GROUP/BUSINESS CREDIT, INC. ("CIT"), individually and as
the Administrative Agent (in such capacity, the "Administrative Agent"), CREDIT
SUISSE FIRST BOSTON, as the documentation agent (in such capacity, the
"Documentation Agent"), DLJ CAPITAL FUNDING, INC., as the syndication agent (in
such capacity, the Syndication Agent" and, together with the Administrative
Agent, individually, a "Agent" and collectively, the "Agents"), and the Lenders
signatory hereto.

                             PRELIMINARY STATEMENTS

       1.     Each of the Borrowers entered into that certain Revolving Credit
              Agreement dated as of July 23, 1999, among the Borrowers, the
              Administrative Agent, the Documentation Agent, the Syndication
              Agent and the other financial institutions that are a signatory
              thereto (the "Existing Credit Agreement"). Capitalized terms used
              but not otherwise defined herein shall have the meanings assigned
              to such terms in the Existing Credit Agreement.

       2.     The Borrowers have requested that certain provisions of the
              Existing Credit Agreement be modified and amended.

       3.     The Borrowers, the Agents, the Documentation Agent and the
              Required Lenders have agreed to amend the Existing Credit
              Agreement on the terms and conditions contained herein.

              NOW, THEREFORE, in consideration of the premises and the mutual
covenants contained herein and in the Existing Credit 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 Article X of the Existing Credit
Agreement. Article X of the Existing Credit Agreement is hereby amended by
adding a new Section 10.17 thereto, to read as follows:

                    SECTION 10.17. ANEXCO Information. (a) Each of the Agents
              and each of the Lenders agrees that (i) it shall hold all
              non-public information of


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              ANEXCO obtained pursuant to this Agreement (the "ANEXCO
              Information"), including account obligor information with respect
              to the accounts receivable of ANEXCO, in strict confidence, (ii)
              it will not disclose any of the ANEXCO Information to any Person
              other than (A) either of the Agents or any Lender, (B) its
              employees who need to know the ANEXCO Information in connection
              with the transactions contemplated by this Agreement, who are
              informed of the confidential nature of the ANEXCO Information and
              who agree to abide by and act in accordance with the terms of
              this Section to the same extent as if they were parties hereto,
              (C) its examiners, outside auditors, counsel and other
              professional advisors in connection with this Agreement, (D) any
              Person that has become, in accordance with the requirements of
              this Agreement, a bona fide transferee, participant or assignee
              of the interests of any Lender under this Agreement and (E) any
              governmental agency or representative thereof as required or
              requested pursuant to legal process, and (iii) it shall use the
              ANEXCO Information only in connection with this Agreement and not
              for any other purpose; provided, however, this Section shall not
              apply (A) if any of the ANEXCO Information (x) was or becomes
              generally available to the public other than by disclosure by the
              Agents or any Lender or any of their respective employees,
              agents, examiners, outside auditors, counsel, other professional
              advisors, transferees, participants or assignees or (y) was or
              becomes available on a non-confidential basis from a source other
              than the Borrowers, ANEXCO or BP, or (B) to the extent reasonably
              required in connection with the enforcement of any Loan Document
              (collectively "Excluded Information").

                    (b) Each of the Agents and each of the Lenders agrees that:

                           (i) it will cause its employees, outside auditors,
                    counsel and other professional advisors to observe the
                    terms of this Section and will be responsible for any
                    breach of this Section;

                          (ii) any outside auditor, counsel or professional
                    advisor (other than those outside auditors, counsel or
                    professional advisors regularly providing such services to
                    such Lender or to the Administrative Agent) to whom it
                    proposes to disclose any ANEXCO Information other than the
                    Excluded Information must be approved by BP or ANEXCO prior
                    to such disclosure, such approval not to be unreasonably
                    withheld or delayed;

                         (iii) prior to disclosing any information to a
                    transferee, participant or assignee pursuant to this
                    Section, it will require such transferee, participant or
                    assignee to agree to be bound by this Section; and


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                          (iv) unless specifically prohibited by applicable law
                    or court order, it will (A) notify BP and ANEXCO of any
                    request by any governmental agency or representative
                    thereof (other than any such request in connection with a
                    routine examination of its financial condition by such
                    governmental agency) for disclosure of any ANEXCO
                    Information other than Excluded Information at least five
                    business days prior to disclosure of such ANEXCO
                    Information other than Excluded Information (or if prior
                    notification of such length is not reasonably practicable
                    under the circumstances, as soon as is reasonably
                    practicable under the circumstances but in any event prior
                    to such disclosure) and (B) permit BP and ANEXCO to file or
                    otherwise make an objection with the relevant governmental
                    agency or representative thereof to the disclosure of such
                    ANEXCO Information.

                    (c) Each of the Agents, the Documentation Agent and each of
              the Lenders acknowledges that the ANEXCO Information other than
              the Excluded Information may be of a competitively sensitive
              nature and agrees to hold all of the ANEXCO Information other
              than the Excluded Information in accordance with its customary
              procedures for handling confidential information of that nature
              and in accordance with safe and sound banking practices.

                    (d) Notwithstanding anything to the contrary contained in
              this Agreement, each of BP and ANEXCO (i) shall be a third party
              beneficiary of this Section and shall be entitled to rights and
              privileges hereof to the extent that (A) any ANEXCO Information
              other than the Excluded Information was obtained by Sterling from
              BP or ANEXCO and disclosed to either of the Agents or any of the
              Lenders or (B) any ANEXCO Information other than the Excluded
              Information is otherwise obtained by either of the Agents or any
              of the Lenders from BP or ANEXCO, and (ii) shall be entitled to
              enforce this Section 10.17 against the Agents and the Lenders to
              the same extent as if BP and ANEXCO were parties hereto.

                    (e) Notwithstanding anything to the contrary contained in
              this Agreement, no amendment, modification or restatement of, or
              waiver under, this Section 10.17 which would adversely affect BP
              or ANEXCO shall be or become effective without the prior written
              consent of BP and ANEXCO.

                    (f) All notices, requests and other communications provided
              to BP or ANEXCO under this Agreement shall be in writing and
              addressed, delivered or transmitted to the following address or
              facsimile number:

                           BP Chemicals Inc.
                           Manager, Planning, Control & Development
                           Nitriles Business Unit
                           Bldg. 605-1, N-3 1561


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                           150 West Warrenville Road
                           Naperville, Illinois  60563-8460
                           Facsimile Number:  (630) 961-7676

              or at such other address or facsimile number as may be designated
              by BP or ANEXCO in a notice to the Administrative Agent. Any
              notice, (i) if mailed and properly addressed with postage prepaid
              or if properly addressed and sent by pre-paid courier service,
              shall be deemed given when it has been received or (ii) if
              transmitted by facsimile, shall be deemed given when transmitted
              (and telephonic confirmation of receipt thereof has been
              received).

              Section 2. Effect of This Amendment. The Existing Credit
Agreement and this Amendment shall be read, taken and construed as one and the
same instrument. Except as expressly modified hereby or by express written
amendments thereof, each of the Loan Documents and each of the other documents
and instruments executed in connection with any of the foregoing are and shall
remain in full force and effect. In the event of a conflict between this
Amendment and any of the foregoing documents, the terms of this Amendment shall
be controlling. Upon the effectiveness of this Amendment, each reference in the
Existing Credit Agreement to "this Agreement" and each reference in each of the
other Loan Documents to "the Credit Agreement" shall mean and be a reference to
the Existing Credit Agreement as amended hereby.

              Section 3. Limitations. The amendments set forth herein are
limited precisely as written and shall not (a) be deemed to be a consent to, or
a waiver or modification of, any other term or condition of any of the Loan
Documents or (b) except as expressly set forth herein, prejudice any right or
rights which the Agents or the Lenders may now have or may have in the future
under or in connection with any of the Loan Documents or any of the other
documents or instruments referred to therein.

              Section 4. Conditions Precedent and Effectiveness. This Amendment
shall not be effective unless and until (a) counterparts hereof executed on
behalf of each Borrower and the Required Lenders (or notice thereof
satisfactory to the Agents) shall have been received by the Syndication Agent
and, upon receipt of such counterparts or notice by the Syndication Agent,
shall be and become effective as of December 17, 1999 (the "Amendment Effective
Date") and (b) the Agents shall have received for the account of each Lender,
all fees, costs and expenses due and payable pursuant to Sections 3.3 and 10.3
of the Credit Agreement or payable hereunder, if then invoiced.

              Section 5. Representations and Warranties. Each of the Borrowers
hereby represents and warrants to the Agents and the Lenders that (a) except as
affected by the transactions contemplated in the Existing Credit Agreement and
this Amendment, each of the representations and warranties made by the
Borrowers in or pursuant to each of the Loan Documents is true and correct in
all material respects as of the Amendment Effective Date, as if made on and as
of such date, except for any representations and warranties made as of a
specified date, which are true and correct in all material respects as of such
specified date, and (b) no Default or Event of Default has occurred and is
continuing as of the Amendment Effective Date.


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              Section 6. Adoption, Ratification and Confirmation of Existing
Credit Agreement. Each of the Borrowers, each of the Agents, the Documentation
Agent and each of the Lenders signatories hereto hereby adopts, ratifies and
confirms the Existing Credit Agreement, as amended hereby, and acknowledges and
agrees that the Existing Credit Agreement, as amended hereby, is and remains in
full force and effect.

              Section 7. Payment of Costs and Expenses. Each Borrower, jointly
and severally, agrees to pay on demand all reasonable expenses of each Agent
(including the reasonable fees and out-of-pocket expenses of Mayer, Brown &
Platt, counsel to the Agents) in connection with (a) the negotiation,
preparation, execution and delivery of this Amendment, whether or not the
transactions contemplated hereby are consummated, and (b) the preparation and
review of the form of any document or instrument relevant to this Amendment.
Each Borrower further jointly and severally agrees to pay, and to save the
Agents, the Documentation Agent and the Lenders harmless from all liability
for, any stamp or other similar Taxes which may be payable in connection with
the execution or delivery of this Amendment.

              Section 8. Severability. Any provision of this Amendment which is
prohibited or unenforceable in any jurisdiction shall, as to such provision and
such jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions of this
Amendment or affecting the validity or enforceability of such provision in any
other jurisdiction.

              Section 9. Headings. The various headings of this Amendment are
inserted for convenience only and shall not affect the meaning or
interpretation of this Amendment or any provisions hereof.

              Section 10. Execution in Counterparts. This Amendment may be
executed by the parties hereto in several counterparts, each of which shall be
deemed to be an original (whether such counterpart is originally executed or an
electronic copy of an original and each party hereto other than the Agents and
Sterling expressly waives its rights to receive originally executed documents)
and all of which shall constitute together but one and the same agreement.

              Section 11. Governing Law; Entire Agreement. THIS AMENDMENT SHALL
BE DEEMED TO BE A CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE
STATE OF NEW YORK, EXCLUDING THE LAW OF CONFLICTS BUT GIVING EFFECT TO FEDERAL
LAWS APPLICABLE TO NATIONAL BANKS. This Amendment, the Existing Credit
Agreement and the other Loan Documents constitute the entire understanding
among the parties hereto and thereto with respect to the subject matter hereof
and thereof and supersede any prior agreements, written or oral, with respect
thereto.

              Section 12. Loan Document Pursuant to Existing Credit Agreement.
This Amendment is a Loan Document pursuant to the Existing Credit Agreement and
shall be construed, administered and applied in accordance with all of the
terms and provisions of the Existing Credit Agreement.


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              IN WITNESS WHEREOF, the parties hereto have caused this Amendment
to be duly executed and delivered by their respective duly authorized officers
as of the Amendment Effective Date.

THE BORROWERS:                STERLING CHEMICALS, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President - Finance
                                         and Chief Financial Officer


                              STERLING CANADA, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President - Finance


                              STERLING CHEMICALS ENERGY, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President


                              STERLING CHEMICALS INTERNATIONAL, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President


                              STERLING FIBERS, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President


                              STERLING PULP CHEMICALS, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President - Finance


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                              STERLING PULP CHEMICALS US, INC.



                              By:
                                  --------------------------------------------
                                    Gary M. Spitz, Vice President - Finance




AGENTS AND LENDERS:           THE CIT GROUP/BUSINESS CREDIT, INC.,
                                  As Administrative Agent and a Lender



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


                              DLJ CAPITAL FUNDING, INC.,
                                  As Syndication Agent



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

                              CREDIT SUISSE FIRST BOSTON,
                                  As Documentation Agent



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



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


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                              IBJ WHITEHALL BUSINESS CREDIT
                                 CORPORATION



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


                              FLEET CAPITAL CORPORATION



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


                              COAST BUSINESS CREDIT,
                                 A Division Of Southern Pacific Bank



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


                              FINOVA CAPITAL CORPORATION



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


                              TEXTRON FINANCIAL CORP.



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


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                              GREEN TREE FINANCIAL SERVICING
                                 CORPORATION



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


                              GMAC BUSINESS CREDIT, LLC



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

                              THE PROVIDENT BANK



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


                              GPSF SECURITIES, INC.



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


                              FOOTHILL CAPITAL CORPORATION



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


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                              CONGRESS FINANCIAL CORPORATION
                                 (SOUTHWEST)



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


                              COMERICA BANK



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


                              KZH STERLING, LLC



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


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