CENTERPOINT ENERGY HOUSTON ELECTRIC, LLC TO JPMORGAN CHASE BANK Trustee ELEVENTH SUPPLEMENTAL INDENTURE Dated as of May 23, 2003

EXHIBIT 4.1

CenterPoint Energy Houston Electric, LLC

1111 Louisiana

Houston, TX 77002

CENTERPOINT ENERGY HOUSTON ELECTRIC, LLC

TO

JPMORGAN CHASE BANK

Trustee

ELEVENTH SUPPLEMENTAL INDENTURE

Dated as of May 23, 2003

Supplementing the General Mortgage Indenture

Dated as of October 10, 2002

THIS INSTRUMENT GRANTS A SECURITY INTEREST BY A PUBLIC UTILITY

THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS

This instrument is being filed pursuant to Chapter 35 of the Texas Business and Commerce Code

ELEVENTH SUPPLEMENTAL INDENTURE, dated as of May 23, 2003, between CENTERPOINT ENERGY HOUSTON ELECTRIC, LLC, a limited liability company organized and existing under the laws of the State of Texas (herein called the “Company”), having its principal office at 1111 Louisiana, Houston, Texas 77002, and JPMORGAN CHASE BANK, a banking corporation duly organized and existing under the laws of the State of New York, as Trustee (herein called the “Trustee”), the office of the Trustee at which on the date hereof its corporate trust business is administered being 600 Travis Street, Suite 1150, Houston, Texas 77002.

RECITALS OF THE COMPANY

WHEREAS, the Company has heretofore executed and delivered to the Trustee a General Mortgage Indenture dated as of October 10, 2002 (the “Indenture”) providing for the issuance by the Company from time to time of its bonds, notes or other evidence of indebtedness to be issued in one or more series (in the Indenture and herein called the “Securities”) and to provide security for the payment of the principal of and premium, if any, and interest, if any, on the Securities; and

WHEREAS, the Company, in the exercise of the power and authority conferred upon and reserved to it under the provisions of the Indenture and pursuant to appropriate resolutions of the Manager, has duly determined to make, execute and deliver to the Trustee this Eleventh Supplemental Indenture to the Indenture as permitted by Sections 201, 301, 403(2) and 1401 of the Indenture in order to establish the form or terms of, and to provide for the creation and issuance of, a twelfth series of Securities under the Indenture in an initial aggregate principal amount of $200,000,000 (such twelfth series being hereinafter referred to as the “Twelfth Series”); and

WHEREAS, all things necessary to make the Securities of the Twelfth Series, when executed by the Company and authenticated and delivered by the Trustee or any Authenticating Agent and issued upon the terms and subject to the conditions hereinafter and in the Indenture set forth against payment therefor the valid, binding and legal obligations of the Company and to make this Eleventh Supplemental Indenture a valid, binding and legal agreement of the Company, have been done;

NOW, THEREFORE, THIS ELEVENTH SUPPLEMENTAL INDENTURE WITNESSETH that, in order to establish the terms of a series of Securities, and for and in consideration of the premises and of the covenants contained in the Indenture and in this Eleventh Supplemental Indenture and for other good and valuable consideration the receipt and sufficiency of which are hereby acknowledged, it is mutually covenanted and agreed as follows:

ARTICLE ONE

DEFINITIONS AND OTHER PROVISIONS

OF GENERAL APPLICATION

Section 101.    Definitions.    Each capitalized term that is used herein and is defined in the Indenture shall have the meaning specified in the Indenture unless such term is otherwise defined herein.

ARTICLE TWO

TITLE, FORM AND TERMS OF THE BONDS

Section 201.    Title of the Bonds.    This Eleventh Supplemental Indenture hereby creates a series of Securities designated as the “5.60% General Mortgage Bonds, Series L, due July 1, 2023” (the “Series L Bonds”) and a series of Securities designated as the “5.60% General Mortgage Bonds, Series L2, due July 1, 2023” (the “Series L2 Bonds” and, together with the Series L Bonds, the “Bonds”). For purposes of the Indenture, the Bonds shall constitute a single series of Securities and, subject to the provisions, including, but not limited to Article Four of the Indenture, the Bonds may be issued in an unlimited principal aggregate amount, although the initial issuance of the Bonds shall be in the principal amount of $200,000,000.

Section 202.    Form and Terms of the Bonds.    The form and terms of the Bonds will be set forth in an Officer’s Certificate delivered by the Company to the Trustee pursuant to the authority granted by this Eleventh Supplemental Indenture in accordance with Sections 201 and 301 of the Indenture.

Section 203.    Treatment of Proceeds of Title Insurance Policy.    Any moneys received by the Trustee as proceeds of any title insurance policy on Mortgaged Property of the Company shall be subject to and treated in accordance with the provisions of Section 607(2) of the Indenture (other than the last paragraph thereof).

ARTICLE THREE

MISCELLANEOUS PROVISIONS

The Trustee makes no undertaking or representations in respect of, and shall not be responsible in any manner whatsoever for and in respect of, the validity or sufficiency of this Eleventh Supplemental Indenture or the proper authorization or the due execution hereof by the Company or for or in respect of the recitals and statements contained herein, all of which recitals and statements are made solely by the Company.

Except as expressly amended and supplemented hereby, the Indenture shall continue in full force and effect in accordance with the provisions thereof and the Indenture is in all respects hereby ratified and confirmed. This Eleventh Supplemental Indenture and all of its provisions shall be

deemed a part of the Indenture in the manner and to the extent herein and therein provided.

This Eleventh Supplemental Indenture shall be governed by, and construed in accordance with, the law of the State of New York.

This Eleventh Supplemental Indenture 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.

IN WITNESS WHEREOF, the parties hereto have caused this Eleventh Supplemental Indenture to be duly executed as of the day and year first above written.

ACKNOWLEDGMENT

On the 21st day of May 2003, before me personally came Marc Kilbride, to me known, who, being by me duly sworn, did depose and say that he resides in Houston, Texas; that he is the Treasurer of CenterPoint Energy Houston Electric, LLC, a Texas limited liability company, the limited liability company described in and which executed the foregoing instrument; and that he signed his name thereto by authority of the sole manager of said limited liability company.

ACKNOWLEDGMENT

On the 21^st day of May 2003, before me personally came Carol Logan, to me known, who, being by me duly sworn, did depose and say that she resides in Houston, Texas; that she is Vice President and Trust Officer of JPMorgan Chase Bank, a banking corporation organized under the State of New York, the Person described in and which executed the foregoing instrument; and that she signed her name thereto by authority of the board of directors of said corporation.