<PAGE>   1
                                                                     Exhibit 4.1


                               FIRST AMENDMENT TO
                      AMENDED AND RESTATED CREDIT AGREEMENT

              THIS FIRST AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT
(this "First Amendment") dated effective as of March 31, 1998 (the "First
Amendment Effective Date") is by and among STERLING CHEMICALS, INC., a Delaware
corporation (the "Company"), CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
individually and as Administrative Agent, and CREDIT SUISSE FIRST BOSTON,
individually and as Documentation Agent, and the other financial institutions
signatories hereto.

                             PRELIMINARY STATEMENTS

       1.     The Company has entered into an Amended and Restated Credit
              Agreement dated as of July 10, 1997 among the Company, Texas
              Commerce Bank National Association (now known as Chase Bank of
              Texas, National Association), individually, as an Issuing Bank and
              as Administrative Agent, Credit Suisse First Boston, individually,
              as an Issuing Bank and as Documentation Agent, and the financial
              institutions parties thereto (the "Original Agreement").
              Capitalized terms used but not otherwise defined herein shall have
              the meanings assigned such terms in the Original Agreement.

       2.     The Company has requested that certain provisions of the Original
              Agreement be modified and amended.

       3.     The Company, the Administrative Agent, the Documentation Agent,
              the Subsidiary Guarantors and the Lenders have agreed to amend the
              Original Agreement on the terms and conditions contained herein.

                                    AGREEMENT

              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 1.01 of the Original Agreement.
Section 1.01 of the Original Agreement is hereby amended by adding the following
new definitions thereto immediately following the definition of "Financing
Documents" contained therein:

              "First Amendment" shall mean the First Amendment to Amended and
       Restated Credit Agreement dated as of March 31, 1998 among the Company,
       the Administrative Agent, the Documentation Agent and the Required
       Lenders.


<PAGE>   2

              Section 2. Amendment of Section 1.01 of the Original Agreement.
The definition of "Agreement" contained in Section 1.01 of the Original
Agreement is hereby amended to read in its entirety as follows:

              "Agreement" shall mean this Amended and Restated Credit Agreement,
       as amended by the First Amendment and as further amended, modified or
       supplemented from time to time.

              Section 3. Amendment of Section 4.09 of the Original Agreement.
The first sentence of Section 4.09 of the Original Agreement is hereby amended
to read in its entirety as follows:

       The Company will use the proceeds of the Loans only for the purposes
       specified in the Introductory Statements to this Agreement; provided,
       however, that in no event shall the Company use the proceeds of any Loan
       for the purpose of making any investment pursuant to Section 5.04(e)(xx).

              Section 4. Amendment of Section 5.03(a) of the Original Agreement.
Section 5.03(a) of the Original Agreement is hereby amended to read in its
entirety as follows:

              (a) Interest Coverage Ratio. Maintain an Interest Coverage Ratio
       of not less than the ratio for each Rolling Period indicated below:

<TABLE>
<CAPTION>

                    Each Rolling Period ending                                  Ratio
                    --------------------------                                  -----
                    <S>                                                         <C> 
                    December 31, 1996                                           1.75
                    March 31, 1997                                              1.75
                    June 30, 1997                                               1.75
                    September 30, 1997                                          1.50
                    December 31, 1997                                           1.35
                    March 31, 1998                                              1.30
                    June 30, 1998                                               1.05
                    September 30, 1998                                          1.00
                    December 31, 1998                                           1.00
                    March 31, 1999                                              1.15
                    June 30, 1999                                               1.30
                    September 30, 1999                                          1.35

                    Each Rolling Period                                         Ratio
                    -------------------                                         -----
                    thereafter                                                  2.50
                    ----------
</TABLE>


                                      -2-
<PAGE>   3


              Section 5. Amendment of Section 5.03(c) of the Original Agreement.
Section 5.03(c) of the Original Agreement is hereby amended to read in its
entirety as follows:

              (c) Fixed Charge Coverage Ratio. Maintain a Fixed Charge Coverage
       Ratio of not less than the ratio for each Rolling Period indicated below:
<TABLE>

                    <S>                                                         <C>
                    Each Rolling Period during
                    --------------------------
                    the period beginning January 1,                             Ratio
                    -------------------------------                             -----
                    1997 through September 30, 1997                             1.05
                    -------------------------------


                    Each Rolling Period ending                                  Ratio
                    --------------------------                                  -----

                    December 31, 1997                                           1.00
                    March 31, 1998                                              0.80
                    June 30, 1998                                               0.75
                    September 30, 1998                                          0.75
                    December 31, 1998                                           0.75
                    March 31, 1999                                              0.90
                    June 30, 1999                                               0.95
                    September 30, 1999                                          1.00

                    Each Rolling Period during
                    --------------------------
                    the Fiscal Years ending                                     Ratio
                    -----------------------                                     -----
                    September 30, 2000                                          1.15
                    ------------------

                    Each Rolling Period                                         Ratio
                    -------------------                                         -----
                    thereafter                                                  1.20
                    ----------


</TABLE>

              Section 6. Amendment of Section 5.03(d) of the Original Agreement.
Section 5.03(d) of the Original Agreement is hereby amended to read in its
entirety as follows:

              (d) Leverage Ratio. Maintain a Leverage Ratio of not greater than
       the ratio for each Rolling Period indicated below:
<TABLE>

                    <S>                                                         <C>
                    Each Rolling Period ending                                  Ratio
                    --------------------------                                  -----

                    December 31, 1996                                           5.25
                    March 31, 1997                                              6.35
                    June 30, 1997                                               7.00
                    September 30, 1997                                          7.00
                    December 31, 1997                                           7.00
                    March 31, 1998                                              8.25
                    June 30, 1998                                               9.25
                    September 30, 1998                                          9.75
                    December 31, 1998                                           9.75

</TABLE>


                                      -3-
<PAGE>   4

<TABLE>

                    <S>                                                         <C>
                    March 31, 1999                                              8.25
                    June 30, 1999                                               7.50
                    September 30, 1999                                          7.00

                    Each Rolling Period during
                    --------------------------
                    the Fiscal Years ending                                     Ratio
                    -----------------------                                     -----

                    September 30, 2000                                          4.00
                    September 30, 2001                                          3.50

                    Each Rolling Period                                         Ratio
                    -------------------                                         -----
                    thereafter                                                  3.00
                    ----------
</TABLE>

              Section 7. Amendment of Section 5.03(e) of the Original Agreement.
Section 5.03(e) of the Original Agreement is hereby amended to read in its
entirety as follows:

              (e) Senior Debt Leverage Ratio. Maintain a Senior Debt Leverage
       Ratio of not greater than the ratio for each Rolling Period indicated
       below:
<TABLE>
<CAPTION>

                    <S>                                                         <C>
                    Each Rolling Period ending                                  Ratio
                    --------------------------                                  -----

                    March 31, 1997                                              3.50
                    June 30, 1997                                               3.50
                    September 30, 1997                                          3.50
                    December 31, 1997                                           3.50
                    March 31, 1998                                              3.50
                    June 30, 1998                                               4.00
                    September 30, 1998                                          4.25
                    December 31, 1998                                           4.25
                    March 31, 1999                                              3.50
                    June 30, 1999                                               3.25

                    Each Rolling Period                                         Ratio
                    -------------------                                         -----
                    thereafter                                                  3.00
                    ----------
</TABLE>

              Section 8. Amendment of Section 5.04(e) of the Original Agreement.
Section 5.04(e) of the Original Agreement is hereby amended by (a) deleting the
word "and" at the end of clause (xviii) thereof, (b) replacing the period at the
end of clause (xix) thereof with "; and" and (c) adding a new clause (xx) to
read in its entirety as follows:

              (xx) investments resulting from purchases after June 30, 1998 of
       shares of Holdco Common Stock pursuant to put options arising under the
       ESOP or the Old ESOP but only to the extent such purchases are required
       by (A) the provisions of the ESOP or the Old ESOP, as the case may be, as
       in effect on January 1, 1997 and (B) Section 409(h)(1)(B) of the Code and
       the regulations thereunder.


                                      -4-
<PAGE>   5

              Section 9. 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 Financing
Documents or (b) except as expressly set forth herein, prejudice any right or
rights which the Lenders may now have or may have in the future under or in
connection with any of the Financing Documents or any of the other documents or
instruments referred to therein. Except as expressly modified hereby or by
express written amendments thereof, each of the Financing 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 First Amendment and any of the foregoing documents, the
terms of this First Amendment shall be controlling.

              Section 10. Conditions Precedent and Effectiveness. This First
Amendment shall not be effective unless this First Amendment has been executed
and delivered by the Required Lenders.

              Section 11. Representations and Warranties. The Company hereby
represents and warrants to the Administrative Agent, the Documentation Agent and
each of the Lenders that (a) except as affected by the transactions contemplated
in the Original Agreement and this First Amendment, each of the representations
and warranties made by the Company and the Subsidiary Guarantors in or pursuant
to each of the Financing Documents is true and correct in all material respects
as of the First 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 First
Amendment Effective Date.

              Section 12. Adoption, Ratification and Confirmation of Original
Agreement. Each of the Company, the Administrative Agent, the Documentation
Agent and each of the Lenders signatories hereto hereby adopts, ratifies and
confirms the Original Agreement, as amended hereby, and acknowledges and agrees
that the Original Agreement, as amended hereby, is and remains in full force and
effect.

              Section 13. Ratification and Affirmation of Subsidiary Guaranty.
Each of the Subsidiary Guarantors hereby expressly (a) acknowledges the terms of
this First Amendment, (b) acknowledges, renews and extends its continued
liability under the Guaranty Agreement to which it is a party and agrees that
such Guaranty Agreement remains in full force and effect and (c) agrees with the
Administrative Agent, the Documentation Agent, each Lender and each Issuing Bank
to promptly pay when due all amounts owing or to be owing by it under such
Guaranty Agreement pursuant to the terms and conditions thereof.

              Section 14. Payment of Expenses. The Company agrees, whether or
not the transactions contemplated hereby shall be consummated, to reimburse and
save the Administrative Agent and the Documentation Agent harmless from and
against liability for the payment of all reasonable out-of-pocket costs and
expenses arising in connection with the preparation, execution, delivery,
amendment, modification, waiver and enforcement of, or the



                                      -5-

<PAGE>   6
preservation of any rights under this First Amendment, including, without
limitation, the reasonable fees and expenses of any local or other counsel for
the Administrative Agent, and all stamp taxes (including interest and penalties,
if any), recording taxes and fees, filing taxes and fees and other charges which
may be payable in respect of, or in respect of any modification of, any of the
Financing Documents. The provisions of this Section shall survive the
termination of the Original Agreement and the repayment of the Loans.

              Section 15. Governing Law. THIS FIRST AMENDMENT AND THE RIGHTS AND
OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND
BE GOVERNED BY THE LAWS OF THE STATE OF NEW YORK (INCLUDING SECTION 5-1401 OF
THE NEW YORK GENERAL OBLIGATION LAW, OR ANY SIMILAR SUCCESSOR PROVISIONS
THERETO, BUT EXCLUDING ALL OTHER CONFLICT-OF-LAWS RULES) AND TO THE EXTENT
CONTROLLING, LAWS OF THE UNITED STATES OF AMERICA.

              Section 16. Descriptive Headings, Etc. The descriptive headings of
the several sections of this First Amendment are inserted for convenience only
and shall not be deemed to affect the meaning or construction of any of the
provisions hereof.

              Section 17. Entire Agreement. This First Amendment and the
documents referred to herein represent the entire understanding of the parties
hereto regarding the subject matter hereof and supersede all prior and
contemporaneous oral and written agreements of the parties hereto with respect
to the subject matter hereof.

              Section 18. Counterparts. This First Amendment may be executed in
any number of counterparts (including by telecopy) and by different parties on
separate counterparts and all of such counterparts shall together constitute one
and the same instrument.


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

COMPANY:                             STERLING CHEMICALS, INC.



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



                                      -6-
<PAGE>   7

ADMINISTRATIVE AGENT                   CHASE BANK OF TEXAS,
DOCUMENTATION AGENT                    NATIONAL ASSOCIATION,
AND THE LENDERS:                       Individually and as Administrative Agent



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

                                       CREDIT SUISSE FIRST BOSTON,
                                       Individually and as Documentation Agent



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



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

                                       ABN AMRO BANK N.V.
                                       Houston Agency

                                       By:   ABN AMRO North America, Inc.,
                                             as Agent



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


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



                                      -7-
<PAGE>   8

                                       THE BANK OF NOVA SCOTIA



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

                                       BANK OF SCOTLAND



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

                                       BHF-BANK AKTIENGESELLSCHAFT



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


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

                                       CIBC, INC.



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


                                      -8-
<PAGE>   9

                                       CREDIT LYONNAIS NEW YORK BRANCH



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

                                       FIRST SOURCE FINANCIAL LLP

                                       By:   First Source Financial, Inc.,
                                             as its Agent/Manager



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

                                       THE FIRST NATIONAL BANK OF CHICAGO



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

                                       THE CIT GROUP/BUSINESS CREDIT, INC.



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

                                       COMERICA BANK



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


                                      -9-
<PAGE>   10

                                       CREDITANSTALT CORPORATE FINANCE, INC.



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


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

                                       HIBERNIA NATIONAL BANK



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

                                       MERITA BANK LTD
                                       New York Branch



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


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



                                      -10-
<PAGE>   11

                                       NATIONAL BANK OF CANADA



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


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

                                       THE LONG-TERM CREDIT BANK OF JAPAN
                                       LIMITED NEW YORK BRANCH



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

                                       OCTAGON CREDIT INVESTORS LOAN
                                       PORTFOLIO (a unit of The Chase Manhattan
                                       Bank)



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

                                       MASSACHUSETTS MUTUAL LIFE INSURANCE
                                       COMPANY



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



                                      -11-

<PAGE>   12

                                       MERRILL LYNCH SENIOR FLOATING RATE
                                       FUND, INC.



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


                                       ML CBO IV (CAYMAN) LTD.

                                       By:   Protective Asset Management L.L.C.,
                                             as Collateral Manager



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

                                       VAN KAMPEN AMERICA CAPITAL PRIME RATE
                                       INCOME TRUST



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

                                       PARIBAS CAPITAL FUNDING LLC



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


                                      -12-
<PAGE>   13

                                       RESTRUCTURED OBLIGATIONS BACKED BY
                                       SENIOR ASSETS B.V.

                                       By:   ABN Trustcompany (Nederland) B.V.,
                                             its Managing Director



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


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

                                       AERIES FINANCE LTD.



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

                                       CAPTIVA FINANCE LTD.



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

                                       CAPTIVA II FINANCE LTD.



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


                                      -13-

<PAGE>   14

                                     CERES FINANCE LTD.



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

                                     MERRILL LYNCH PRIME RATE PORTFOLIO

                                     By:   Merrill Lynch Asset Management, L.P.,
                                             as Investment Advisor



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

                                     SKANDINAVISKA ENSKILDA BANKEN
                                     CORPORATION



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

                                     THE CHASE MANHATTAN BANK



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




                                      -14-
<PAGE>   15




SUBSIDIARY GUARANTORS:                STERLING CHEMICALS INTERNATIONAL, INC.
                                      STERLING CHEMICALS ENERGY, INC.
                                      STERLING FIBERS, INC.



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


                                      STERLING CANADA, INC.
                                      STERLING PULP CHEMICALS US, INC.
                                      STERLING PULP CHEMICALS, INC.



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



                                      -15-