<PAGE>

                                                                     EXHIBIT 4.2

________________________________________________________________________________



                         FIRST SUPPLEMENTAL INDENTURE

                         dated as of October 23, 2001

                                      to


                                TRUST INDENTURE

                         dated as of October 23, 2001


                                     among


                               ELWOOD ENERGY LLC

                                      and

                            BANK ONE TRUST COMPANY,
                       NATIONAL ASSOCIATION, as Trustee


________________________________________________________________________________
<PAGE>

          FIRST SUPPLEMENTAL INDENTURE, dated as of October 23, 2001 (this
"First Supplemental Indenture"), to the Trust Indenture, dated as of October 23,
 ----------------------------
2001 (the "Original Indenture"), between ELWOOD ENERGY LLC, a Delaware limited
           ------------------
liability company (together with its successors and assigns, the "Issuer") and
                                                                  ------
BANK ONE TRUST COMPANY, NATIONAL ASSOCIATION, a national banking corporation
(the "Trustee").
      -------

          WHEREAS, the Issuer and the Trustee have heretofore executed and
delivered the Original Indenture to provide for the issuance from time to time
of Bonds (as defined in the Original Indenture) of the Issuer, to be issued in
one or more series;

          WHEREAS, Sections 2.1, 2.3 and 12.1 of the Original Indenture provide,
                   ------------  ---     ----
among other things, that the Issuer and the Trustee may enter into indentures
supplemental to the Original Indenture for, among other things, the purpose of
establishing the designation, form, terms and provisions of Bonds of any series
as permitted by Sections 2.1, 2.3 and 12.1 of the Original Indenture;
                ------------  ---     ----

          WHEREAS, the Issuer (i) desires the issuance of a series of Bonds to
be designated as hereinafter provided and (ii) has requested the Trustee to
enter into this First Supplemental Indenture for the purpose of establishing the
designation, form, terms and provisions of the Bonds of such series;

          WHEREAS, all action on the part of the Issuer necessary to authorize
the issuance of said Bonds under the Original Indenture and this First
Supplemental Indenture (the Original Indenture, as supplemented by this First
Supplemental Indenture, being hereinafter called the "Indenture") has been duly
                                                      ---------
taken.

          NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

          That, in order to establish the designation, form, terms and
provisions of, and to authorize the authentication and delivery of, said Bonds,
and in consideration of the acceptance of said Bonds by the Holders thereof and
of other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the parties hereto hereby agree as follows:

                                   ARTICLE I

                                  DEFINITIONS
                                  -----------
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          (a)  Capitalized terms used herein and not otherwise defined herein
shall have the respective meanings ascribed thereto in the Original Indenture.

          (b)  The rules of interpretation set forth in the Original Indenture
shall be applied hereto as if set forth in full herein.

          (c)  For all purposes of this First Supplemental Indenture, except as
otherwise expressly provided or unless the context otherwise requires, the
following terms shall have the following respective meanings (such meanings
shall apply equally to both the singular and plural forms of the respective
terms):

          "Initial Bonds" shall mean the Senior Secured Bonds due 2026.
           -------------

          "Make-Whole Premium" shall mean an amount equal to the Discounted
           ------------------
Present Value calculated on the third Business Day before the Redemption Date
for any Bond subject to redemption less the unpaid principal amount of such
Bond; provided, that the Make-Whole Premium shall not be less than zero.  For
      --------
purposes of this definition, "Discounted Present Value" of any Bond subject to
                              ------------------------
redemption shall be equal to the present value of all principal and interest
payments scheduled to become due in respect of such Bond after the date of such
redemption (excluding accrued interest to the date of redemption) discounted to
the date of redemption on a semiannual basis (assuming a 360-day year consisting
of twelve 30-day months), at a discount rate equal to the sum of (1) the yield
to maturity on the United States treasury securities having an interpolated
maturity equal to the remaining average life of such Bond and trading in the
secondary market at the price closest to par and (2) fifty (50) basis points;
provided, however, that if there is no United States treasury security having an
--------  -------
interpolated maturity equal to the remaining average life of such Bond, such
discount rate shall be calculated using a yield to maturity interpolated or
extrapolated on a straight-line basis (rounding to the nearest month, if
necessary) from the yields to maturity for two United States treasury securities
having average lives most closely corresponding to the remaining average life of
such Bond and trading in the secondary market at the price closest to par.

          "Senior Secured Bonds due 2026" shall have the meaning ascribed
           -----------------------------
thereto in Section 2.1(a) hereof.
           --------------

                                  ARTICLE II

                            THE TERMS OF THE BONDS
                            ----------------------
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          SECTION 2.1.    Terms of 8.159% Senior Secured Bonds due July 5, 2026.
                          -----------------------------------------------------

          (a)  There is hereby created one series of Bonds designated: 8.159%
Senior Secured Bonds due July 5, 2026, in the aggregate principal amount of
$402,000,000 (the "Senior Secured Bonds due 2026"). The Senior Secured Bonds due
                   -----------------------------
2026 may forthwith be executed by the Issuer and delivered to the Trustee for
authentication and delivery by the Trustee in accordance with the provisions of
Section 2.4 of the Original Indenture.
-----------

          (b)  Each of the Senior Secured Bonds due 2026 shall have and be
subject to such other terms as provided in the Indenture and shall be evidenced
by a Bond in the form of Exhibit E to the Original Indenture.
                         ---------

          SECTION 2.2.    Interest and Principal.
                          ----------------------

          Each Initial Bond shall bear interest on the unpaid principal amount
thereof from time to time outstanding from the date thereof until such amount is
paid in full at a rate of 8.159% per annum.  The principal amount of each
Initial Bond shall be due and payable in installments as set forth below:


                  Scheduled                  Percentage of
                   Payment                    Principal
                      Date                   Amount Payable
                   -------                 ----------------
              January 5, 2002                    1.393%
              July 5, 2002                       0.632%
              January 5, 2003                    2.903%
              July 5, 2003                       0.530%
              January 5, 2004                    2.998%
              July 5, 2004                       0.669%
              January 5, 2005                    3.194%
              July 5, 2005                       0.978%
              January 5, 2006                    3.478%
              July 5, 2006                       1.100%
              January 5, 2007                    3.460%
              July 5, 2007                       1.179%
              January 5, 2008                    3.644%
              July 5, 2008                       1.361%
<PAGE>

              January 5, 2009                    3.801%
              July 5, 2009                       1.542%
              January 5, 2010                    4.007%
              July 5, 2010                       1.639%
              January 5, 2011                    4.139%
              July 5, 2011                       1.833%
              January 5, 2012                    4.443%
              July 5, 2012                       2.313%
              January 5, 2013                    5.061%
              July 5, 2013                       0.093%
              January 5, 2014                    1.949%
              July 5, 2014                       0.014%
              January 5, 2015                    1.852%
              July 5, 2015                       0.018%
              January 5, 2016                    2.057%
              July 5, 2016                       0.013%
              January 5, 2017                    1.421%
              July 5, 2017                       0.064%
              January 5, 2018                    3.212%
              July 5, 2018                       0.081%
              January 5, 2019                    3.592%
              July 5, 2019                       0.042%
              January 5, 2020                    3.846%
              July 5, 2020                       0.265%
              January 5, 2021                    4.879%
              July 5, 2021                       0.130%
              January 5, 2022                    6.410%
              July 5, 2022                       0.401%
              January 5, 2023                    4.991%
              July 5, 2023                       0.161%
              January 5, 2024                    2.366%
              July 5, 2024                       0.192%
              January 5, 2025                    2.991%
              July 5, 2025                       0.291%
              January 5, 2026                    1.943%
              July 5, 2026                       0.429%

          Payment of principal of and interest on each Bond of the series
created hereby shall be made (a) if the Issuer so elects, by check mailed to the
Holder at his or her registered address, (b) otherwise as provided in Section
                                                                      -------
2.11 of the
----

                                       4
<PAGE>

Original Indenture or (c) upon application by a record Holder of at least
$1,000,000 in aggregate principal amount of Initial Bonds to the Trustee not
later than 15 days prior to the applicable Payment Date, by wire transfer to an
account maintained by such record Holder with a bank in The City of New York;
provided that the final installment of principal payable with respect to each
--------
Bond of the series created hereby shall be payable as provided in Section 6.5 of
                                                      --------
the Original Indenture (in the case of any such Bond redeemed) or payable upon
presentation and surrender of each such Bond at the Place of Payment.

          SECTION 2.3.    Optional Redemption. The Bonds may be redeemed at the
                          -------------------
option of the Issuer in accordance with and subject to Section 6.3 of the
Original Indenture as follows:

               (i)   The Outstanding Bonds may be redeemed prior to maturity, as
a whole or in part ratably, at any time, at a Redemption Price equal to the
outstanding principal amount of the Bonds being redeemed, plus accrued and
unpaid interest thereon to but not including the Redemption Date, plus the Make-
Whole Premium, upon notice given by the Issuer to the Holders of the Bonds not
less than 30 nor more than 60 days prior to the Redemption Date. Notwithstanding
Section 6.4 of the Original Indenture, the notice of redemption under this
Section 2.3 or under Section 2.4(b) need not set forth the Redemption Price but
-----------          --------------
only the manner of calculation thereof. The Issuer shall notify the Trustee of
the Redemption Price promptly after the calculation thereof, and the Trustee
shall have no responsibility for such calculation.

               (ii)  All proceeds received by the Trustee from or on behalf of
the Issuer identified as proceeds for an optional redemption of the Bonds under
this Section 2.3(a) shall be applied by the Trustee to the redemption of such
     --------------
Bonds on the Redemption Date thereof.

          SECTION 2.4.   Mandatory Redemption. The Bonds are subject to
                         --------------------
mandatory redemption in accordance with and subject to the provisions of Section
6.3 of the Original Indenture as follows:

          (a)  Mandatory Redemption Without Make-Whole Premium. The Bonds will
               -----------------------------------------------
be subject to mandatory redemption as follows:

          (i)  Loss Event With No Restoration of Project. In accordance with and
               -----------------------------------------
     subject to the terms of Section 3.10(a)(i) of the Deposit and Disbursement
     Agreement, if (A) a Loss Event occurs and (B) either (x) the Issuer

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<PAGE>

     determines not to Restore the Project or (y) the Issuer determines that the
     Project cannot be Restored to permit operation of the Project on a
     Commercially Feasible Basis, then all Loss Proceeds in excess of $5,000,000
     received by the Issuer in connection with such Loss Event shall be used to
     redeem the Bonds pro rata with the other Senior Secured Obligations, at a
     Redemption Price equal to the outstanding principal amount of the Bonds
     being redeemed, plus accrued and unpaid interest thereon to but not
     including the Redemption Date.

          (ii)  Loss Event With Restoration of Project. In accordance with and
                --------------------------------------
     subject to the terms of Section 3.10 (a)(ii) of the Deposit and
     Disbursement Agreement, if (A) a Loss Event occurs, (B) the Issuer receives
     Loss Proceeds in respect of such Loss Event and (C) the Issuer determines
     that the Project can be Restored to permit operation of the Project on a
     Commercially Feasible Basis, then upon completion of any Restoration Work,
     all such Loss Proceeds in excess of $5,000,000 received by Issuer in
     connection with such Loss Event remaining after giving effect to the cost
     of the Restoration shall be used to redeem the Bonds pro rata with the
     other Senior Secured Obligations, at a Redemption Price equal to the
     outstanding principal amount of the Bonds being redeemed, plus accrued and
     unpaid interest thereon to but not including the Redemption Date.

          (iii) Receipt of Buy-Out Proceeds. In accordance with and subject to
                ---------------------------
     the terms of Section 3.10(b) of the Deposit and Disbursement Agreement, if
     (A) the aggregate amount of Buy-Out Proceeds received by or on behalf of
     the Issuer in connection with an Involuntary Buy-Out or Involuntary Buy-
     Outs exceeds $10,000,000 and (B) any Rating Agency does not confirm in
     writing that such Involuntary Buy-Out or Involuntary Buy-Outs will not
     result in a Rating Downgrade by such Rating Agency, then all such Buy-Out
     Proceeds received by the Issuer in connection with such Involuntary Buy-Out
     or Involuntary Buy-Outs in excess of $10,000,000 shall be used to redeem
     the Bonds pro rata with the other Senior Secured Obligations, at a
     Redemption Price equal to the outstanding principal amount of the Bonds
     being redeemed, plus accrued and unpaid interest thereon to but not
     including the Redemption Date.

         (iv)   Proceeds of Permitted Asset Dispositions. In accordance with and
                ----------------------------------------
     subject to the terms of Section 3.10(c) of the Deposit and Disbursement
     Agreement, all Asset Sale Proceeds in excess of $5,000,000 received by the
     Issuer in connection with a disposition of assets permitted by Section
                                                                    -------
     5.1(g)
     ------

                                       6
<PAGE>

     of the Indenture shall be used to redeem the Bonds pro rata with the other
     Senior Secured Obligations, at a Redemption Price equal to the outstanding
     principal amount of the Bonds being redeemed, plus accrued and unpaid
     interest thereon to but not including the Redemption Date.

          (b)  Mandatory Redemption With Make Whole Premium. In accordance with
               --------------------------------------------
and subject to the terms of Section 3.10(b) of the Deposit and Disbursement
Agreement, if (A) the aggregate amount of Buy-Out Proceeds received by or on
behalf of the Issuer in connection with a Voluntary Buy-Out or Voluntary Buy-
Outs exceeds $10,000,000 and (B) any Rating Agency does not confirm in writing
that such Voluntary Buy-Out or Voluntary Buy-Outs will not result in a Rating
Downgrade by such Rating Agency, then all such Buy-Out Proceeds received by the
Issuer in connection with such Voluntary Buy-Out or Voluntary Buy-Outs in excess
of $10,000,000 shall be used to redeem the Bonds pro rata with the other Senior
Secured Obligations, at a Redemption Price equal to the outstanding principal
amount of the Bonds being redeemed, plus accrued and unpaid interest thereon to
but not including the Redemption Date, plus the Make-Whole Premium.

          SECTION 2.5.    Restrictions on Transfer and Exchange of Initial
                          ------------------------------------------------
Bonds. The Initial Bonds shall be represented by one or more Restricted Global
-----
Bonds registered in the name of the nominee for the Registered Depositary.
Interests in the Initial Bonds may be transferred only in accordance with the
applicable procedures set forth in the Original Indenture and the rules of the
Registered Depositary and, in the case of a Regulation S Global Bond, the
Euroclear System and Clearstream Banking, societe anonyme, as applicable.

                             ARTICLE III

                             MISCELLANEOUS
                             -------------

          SECTION 3.1.    Execution of Supplemental Indenture.
                          -----------------------------------

          This First Supplemental Indenture is executed and shall be construed
as an indenture supplemental to the Original Indenture and, as provided in the
Original Indenture, this First Supplemental Indenture forms a part thereof.

          SECTION 3.2.    Concerning the Trustee.
                          ----------------------

          The recitals contained herein and in the Bonds of the series created
hereby, except with respect to the Trustee's certificates of authentication,
shall be

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<PAGE>

taken as the statements of the Issuer, and the Trustee assumes no responsibility
for the correctness of the same. The Trustee makes no representations as to the
validity or sufficiency of this First Supplemental Indenture or of the Bonds of
the series created hereby.

          SECTION 3.3.    Counterparts.
                          ------------

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

          SECTION 3.4.    Governing Law.
                          -------------

          THIS FIRST SUPPLEMENTAL INDENTURE AND EACH BOND OF THE SERIES CREATED
HEREUNDER SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF
THE STATE OF NEW YORK.


        [THE REMAINDER OF THIS PAGE HAS INTENTIONALLY BEEN LEFT BLANK.]

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<PAGE>

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


                         ELWOOD ENERGY LLC


                         By:  /s/ Don Burnette
                              ------------------------------------
                              Name: Don Burnette
                              Title: Authorized Representative



                         BANK ONE TRUST COMPANY, NATIONAL ASSOCIATION, as
                         Trustee


                         By:  /s/ Benita A. Pointer
                              ------------------------------------
                              Name: Benita A. Pointer
                              Title: Account Executive