Document:

<PAGE>

                                                                 EXHIBIT 4.11(a)

                           LYONDELL CHEMICAL COMPANY,

                     THE SUBSIDIARY GUARANTORS party hereto

                                       and

                              THE BANK OF NEW YORK,

                                     Trustee

                             SUPPLEMENTAL INDENTURE

                                   Dated as of

                                  July 3, 2002

                                       to

                                    INDENTURE

                                   Dated as of

                                  May 17, 1999

<PAGE>

          THIS SUPPLEMENTAL INDENTURE (this "Supplement"), dated as of July 3,
2002 (the "Closing Date"), among Lyondell Chemical Company, a Delaware
corporation ("Lyondell"), the Subsidiary Guarantors party hereto, and The Bank
of New York, as trustee (the "Trustee"), supplements the Indenture dated as of
May 17, 1999, among Lyondell, the Subsidiary Guarantors party thereto and the
Trustee, pursuant to which the 9.625% Senior Secured Notes, Series A, Due 2007
(the "Notes") were issued and are outstanding (the "Indenture").

                                    RECITALS

          WHEREAS, Lyondell has executed and delivered to the Trustee the
Indenture, providing for the issuance of the Notes as provided in the Indenture
and guaranteed by the Subsidiary Guarantors to the extent provided therein;

          WHEREAS, Section 9.02 of the Indenture provides that, subject to
certain conditions, Lyondell, the Trustee and any Subsidiary Guarantor may amend
or supplement the Indenture with the written consent of the Holders of not less
than a majority in aggregate principal amount of the Outstanding Notes; and

          WHEREAS, pursuant to Lyondell's Consent Solicitation Statement dated
June 19, 2002, as amended, the written consent of the Holders of not less than a
majority in aggregate principal amount of the Notes has been obtained to effect
changes to the Indenture amending Sections 1.01, 4.07(b)(ix) and 4.09(b)(i) of
the Indenture.

          NOW, THEREFORE, THIS SUPPLEMENT WITNESSETH:

          In consideration of the premises and other good and valuable
consideration, the parties hereto hereby agree, for the equal and proportionate
benefit of the respective Holders from time to time of the Notes, as follows:

                                   SECTION ONE

1.1  Capitalized terms used and not otherwise defined herein have the respective
     meanings assigned to such terms in the Indenture.

1.2  The Trustee makes no representations as to the validity or sufficiency of
     this Supplement. The recitals herein are deemed to be those of Lyondell.

                                   SECTION TWO

                                   AMENDMENTS

2.1  Section 1.01 of the Indenture shall be amended to add the following
     sentence at the end of the definition of "Subsidiary" currently set forth
     in the Indenture:

     No Specified Joint Venture that otherwise would be a "Subsidiary" under
     this definition shall be deemed to be or become a Subsidiary or a
     Restricted Subsidiary until such

<PAGE>

     designation would not result in a Default under Section 4.06 (provided
     that, if (i) such Specified Joint Venture would otherwise be or become a
     "Subsidiary" as a result of an Investment by the Company or any Restricted
     Subsidiary made after June 12, 2002, and (ii) such Investment is not made
     in exchange for, or out of the net cash proceeds of the substantially
     concurrent sale (other than to a Subsidiary or Joint Venture of the
     Company) of, Qualified Equity Interests of the Company, then this sentence
     shall not apply); at such time as the designation of such Specified Joint
     Venture would not result in a Default under Section 4.06, such Specified
     Joint Venture shall automatically be a Subsidiary and a Restricted
     Subsidiary (unless designated as an Unrestricted Subsidiary).

2.2  Section 4.07(b)(ix) of the Indenture shall be amended to read in its
     entirety as follows:

     (ix) the payment of dividends on the Company's common stock at a rate not
     to exceed $0.90 per share per annum (such $0.90 amount to be appropriately
     adjusted to reflect any stock split, reverse stock split, stock dividend or
     similar transaction made after the Issue Date so that the aggregate amount
     of dividends payable after such transaction is the same as the amount
     payable immediately prior to such transaction);

2.3  Section 4.09(b)(i) of the Indenture shall be amended to read in its
     entirety as follows:

     (b)  Within 360 days after the receipt of any Net Proceeds from an Asset
     Sale, the Company may apply such Net Proceeds, at its option:

          (i)  to permanently repay Senior Indebtedness (and to correspondingly
               reduce commitments with respect thereto in the case of revolving
               borrowings) of the Company or a Subsidiary Guarantor or
               Indebtedness (and to correspondingly reduce commitments with
               respect thereto in the case of revolving borrowings) of any
               Restricted Subsidiary that is not a Subsidiary Guarantor;
               provided that, so long as the provisions of Section 4.12 are in
               effect, only (A) repayment of Senior Indebtedness incurred
               under the Existing Credit Facility (but not any refinancing
               thereof other than a credit facility with commercial banks and
               other lenders) or (B) if a Restricted Subsidiary that is not a
               Subsidiary Guarantor has consummated the Asset Sale, repayment of
               Indebtedness of such Restricted Subsidiary, with a corresponding
               reduction in commitments with respect thereto in the case of
               revolving borrowings (provided that the aggregate of all
               repayment of Indebtedness by any Restricted Subsidiary under this
               Section 4.09(b)(i)(B) shall not exceed the amount of Indebtedness
               of such Restricted Subsidiary (including in Indebtedness, for
               purposes of this Section 4.09(b)(i)(B) only, the undrawn portion
               of any revolving credit facility of such Restricted Subsidiary)
               as of June 30, 2002), shall constitute a repayment of
               Indebtedness permitted pursuant to this clause (i); or

                                        2

<PAGE>

                                  SECTION THREE

                                  RATIFICATION

          Except as expressly amended and supplemented in this Supplement, the
Indenture shall remain unchanged and in full force and effect. This Supplement
shall be construed as supplemental to the Indenture and shall form a part
thereof.

                                  SECTION FOUR

                                  GOVERNING LAW

          This Supplement shall be governed by and construed in accordance with
the laws of the State of New York applicable to agreements made and to be
performed therein.

                                  SECTION FIVE

                                  COUNTERPARTS

          This instrument may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all such counterparts
shall together constitute but one and the same instrument.

                                        3

<PAGE>

          IN WITNESS WHEREOF, the parties have duly executed and delivered this
Supplemental Indenture or have caused this Supplemental Indenture to be duly
executed on their respective behalf by their respective officers thereunto duly
authorized, as of the day and year first written above.

                                       LYONDELL CHEMICAL COMPANY

                                       By:/s/ Karen A. Twitchell
                                          --------------------------------------
                                       Name: Karen A. Twitchell
                                       Title: Vice President and Treasurer

                                       ARCO CHEMICAL TECHNOLOGY, INC., as a
                                       Subsidiary Guarantor

                                       By:/s/ Francis P. McGrail
                                          --------------------------------------
                                       Name: Francis P. McGrail
                                       Title: President and Treasurer

                                       ARCO CHEMICAL TECHNOLOGY, L.P., as a
                                       Subsidiary Guarantor
                                       By:  ARCO Chemical Technology Management,
                                       Inc., its General Partner

                                       By:/s/ Francis P. McGrail
                                          --------------------------------------
                                       Name: Francis P. McGrail
                                       Title: President and Treasurer

                                       LYONDELL CHEMICAL NEDERLAND,
                                       LTD., as a Subsidiary Guarantor

                                       By:/s/ Karen A. Twitchell
                                          --------------------------------------
                                       Name:  Karen A. Twitchell
                                       Title:  Vice President and Treasurer

                                       THE BANK OF NEW YORK, as Trustee

                                       By:/s/ Van K. Brown
                                          --------------------------------------
                                       Name:  Van K. Brown
                                       Title:  Vice President<PAGE>

                                                                 EXHIBIT 4.12(a)

                           LYONDELL CHEMICAL COMPANY,

                     THE SUBSIDIARY GUARANTORS party hereto

                                       and

                              THE BANK OF NEW YORK,

                                     Trustee

                             SUPPLEMENTAL INDENTURE

                                   Dated as of

                                  July 3, 2002

                                       to

                                    INDENTURE

                                   Dated as of

                                  May 17, 1999

<PAGE>

          THIS SUPPLEMENTAL INDENTURE (this "Supplement"), dated as of July 3,
2002 (the "Closing Date"), among Lyondell Chemical Company, a Delaware
corporation ("Lyondell"), the Subsidiary Guarantors party hereto, and The Bank
of New York, as trustee (the "Trustee"), supplements the Indenture dated as of
May 17, 1999, among Lyondell, the Subsidiary Guarantors party thereto and the
Trustee, pursuant to which the 9.875% Senior Secured Notes, Series B, Due 2007
(the "Notes") were issued and are outstanding (the "Indenture").

                                    RECITALS

          WHEREAS, Lyondell has executed and delivered to the Trustee the
Indenture, providing for the issuance of the Notes as provided in the Indenture
and guaranteed by the Subsidiary Guarantors to the extent provided therein;

          WHEREAS, Section 9.02 of the Indenture provides that, subject to
certain conditions, Lyondell, the Trustee and any Subsidiary Guarantor may amend
or supplement the Indenture with the written consent of the Holders of not less
than a majority in aggregate principal amount of the Outstanding Notes; and

          WHEREAS, pursuant to Lyondell's Consent Solicitation Statement dated
June 19, 2002, as amended, the written consent of the Holders of not less than a
majority in aggregate principal amount of the Notes has been obtained to effect
changes to the Indenture amending Sections 1.01, 4.07(b)(ix) and 4.09(b)(i) of
the Indenture.

          NOW, THEREFORE, THIS SUPPLEMENT WITNESSETH:

          In consideration of the premises and other good and valuable
consideration, the parties hereto hereby agree, for the equal and proportionate
benefit of the respective Holders from time to time of the Notes, as follows:

                                   SECTION ONE

1.1  Capitalized terms used and not otherwise defined herein have the respective
     meanings assigned to such terms in the Indenture.

1.2  The Trustee makes no representations as to the validity or sufficiency of
     this Supplement. The recitals herein are deemed to be those of Lyondell.

                                   SECTION TWO

                                   AMENDMENTS

2.1  Section 1.01 of the Indenture shall be amended to add the following
     sentence at the end of the definition of "Subsidiary" currently set forth
     in the Indenture:

     No Specified Joint Venture that otherwise would be a "Subsidiary" under
     this definition shall be deemed to be or become a Subsidiary or a
     Restricted Subsidiary until such

<PAGE>

     designation would not result in a Default under Section 4.06 (provided
     that, if (i) such Specified Joint Venture would otherwise be or become a
     "Subsidiary" as a result of an Investment by the Company or any Restricted
     Subsidiary made after June 12, 2002, and (ii) such Investment is not made
     in exchange for, or out of the net cash proceeds of the substantially
     concurrent sale (other than to a Subsidiary or Joint Venture of the
     Company) of, Qualified Equity Interests of the Company, then this sentence
     shall not apply); at such time as the designation of such Specified Joint
     Venture would not result in a Default under Section 4.06, such Specified
     Joint Venture shall automatically be a Subsidiary and a Restricted
     Subsidiary (unless designated as an Unrestricted Subsidiary).

2.2  Section 4.07(b)(ix) of the Indenture shall be amended to read in its
     entirety as follows:

     (ix) the payment of dividends on the Company's common stock at a rate not
     to exceed $0.90 per share per annum (such $0.90 amount to be appropriately
     adjusted to reflect any stock split, reverse stock split, stock dividend or
     similar transaction made after the Issue Date so that the aggregate amount
     of dividends payable after such transaction is the same as the amount
     payable immediately prior to such transaction);

2.3  Section 4.09(b)(i) of the Indenture shall be amended to read in its
     entirety as follows:

     (b)  Within 360 days after the receipt of any Net Proceeds from an Asset
     Sale, the Company may apply such Net Proceeds, at its option:

          (i)  to permanently repay Senior Indebtedness (and to correspondingly
               reduce commitments with respect thereto in the case of revolving
               borrowings) of the Company or a Subsidiary Guarantor or
               Indebtedness (and to correspondingly reduce commitments with
               respect thereto in the case of revolving borrowings) of any
               Restricted Subsidiary that is not a Subsidiary Guarantor;
               provided that, so long as the provisions of Section 4.12 are in
               effect, only (A) repayment of Senior Indebtedness incurred under
               the Existing Credit Facility (but not any refinancing thereof
               other than a credit facility with commercial banks and other
               lenders) or (B) if a Restricted Subsidiary that is not a
               Subsidiary Guarantor has consummated the Asset Sale, repayment of
               Indebtedness of such Restricted Subsidiary, with a corresponding
               reduction in commitments with respect thereto in the case of
               revolving borrowings (provided that the aggregate of all
               repayment of Indebtedness by any Restricted Subsidiary under this
               Section 4.09(b)(i)(B) shall not exceed the amount of Indebtedness
               of such Restricted Subsidiary (including in Indebtedness, for
               purposes of this Section 4.09(b)(i)(B) only, the undrawn portion
               of any revolving credit facility of such Restricted Subsidiary)
               as of June 30, 2002), shall constitute a repayment of
               Indebtedness permitted pursuant to this clause (i); or

                                        2

<PAGE>

                                  SECTION THREE

                                  RATIFICATION

          Except as expressly amended and supplemented in this Supplement, the
Indenture shall remain unchanged and in full force and effect. This Supplement
shall be construed as supplemental to the Indenture and shall form a part
thereof.

                                  SECTION FOUR

                                  GOVERNING LAW

          This Supplement shall be governed by and construed in accordance with
the laws of the State of New York applicable to agreements made and to be
performed therein.

                                  SECTION FIVE

                                  COUNTERPARTS

          This instrument may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all such counterparts
shall together constitute but one and the same instrument.

                                        3

<PAGE>

          IN WITNESS WHEREOF, the parties have duly executed and delivered this
Supplemental Indenture or have caused this Supplemental Indenture to be duly
executed on their respective behalf by their respective officers thereunto duly
authorized, as of the day and year first written above.

                                       LYONDELL CHEMICAL COMPANY

                                       By:/s/ Karen A. Twitchell
                                          --------------------------------------
                                       Name:  Karen A. Twitchell
                                       Title:  Vice President and Treasurer

                                       ARCO CHEMICAL TECHNOLOGY, INC., as a
                                       Subsidiary Guarantor

                                       By:/s/ Francis P. McGrail
                                          --------------------------------------
                                       Name: Francis P. McGrail
                                       Title: President and Treasurer

                                       ARCO CHEMICAL TECHNOLOGY, L.P., as a
                                       Subsidiary Guarantor
                                       By:  ARCO Chemical Technology Management,
                                       Inc., its General Partner

                                       By:/s/ Francis P. McGrail
                                          --------------------------------------
                                       Name: Francis P. McGrail
                                       Title: President and Treasurer

                                       LYONDELL CHEMICAL NEDERLAND,
                                       LTD., as a Subsidiary Guarantor

                                       By:/s/ Karen A. Twitchell
                                          --------------------------------------
                                       Name:  Karen A. Twitchell
                                       Title:  Vice President and Treasurer

                                       THE BANK OF NEW YORK, as Trustee

                                       By:/s/ Van K. Brown
                                          --------------------------------------
                                       Name:   Van K. Brown
                                       Title:  Vice President

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