<PAGE>
                                                                 Exhibit 10.2(a)
                                                                  Conformed Copy


                          FIRST SUPPLEMENTAL INDENTURE

      FIRST SUPPLEMENTAL INDENTURE (this "Supplemental Indenture"), dated as of
January 14, 2002, is made by and among Charter Communications Holdings, LLC, a
Delaware limited liability company (and any successor in interest thereto, the
"Company"), Charter Communications Holdings Capital Corporation, a Delaware
corporation (and any successor in interest thereto, "Charter Capital" and
together with the Company, the "Issuers"), and BNY Midwest Trust Company, as
trustee (the "Trustee").

                                   WITNESSETH:

      WHEREAS, the Issuers and the Trustee have entered into an Indenture dated
as of May 15, 2001 (the "Indenture"), governing the Issuers' 9.625% Senior Notes
due 2009 (the "Notes");

      WHEREAS, Section 2.02 of the Indenture provides for the issuance of
Additional Notes (as defined in Section 1.01 of the Indenture), and 9.01(c) of
the Indenture permits supplementing the Indenture to provide for or confirm the
issuance of Additional Notes without the consent of Holders;

      WHEREAS, the Issuers now desire to issue $350,000,000 of Additional
Notes pursuant to the Indenture;

      WHEREAS, all things necessary to make this Supplemental Indenture a valid
supplement to the Indenture according to its terms and the terms of the
Indenture have been done.

      NOW, THEREFORE, the parties hereto agree as follows:

      Section 1. Definitions. All capitalized terms used herein without
definition herein shall have the respective meanings ascribed to such terms in
the Indenture. The rules of construction and interpretation set forth in
Sections 1.02 through 1.04 and Article 10 of the Indenture shall likewise govern
this Supplemental Indenture.

      Section 2. Issuance of Additional Notes. This Supplemental Indenture
hereby provides for and confirms the issuance of $350,000,000 of Additional
Notes pursuant to the Indenture, to be "Notes" for all purposes of the Indenture
from their date of issuance.

      Section 3. Governing Law. The internal laws of the State of New York shall
govern and be used to construe this Supplemental Indenture and the Additional
Notes without giving effect to the applicable principles of conflicts of laws to
the extent that the application of the laws of another jurisdiction would be
required thereby. Each of the parties hereto agrees to submit to the
jurisdiction of the courts of the State of New York in any action or proceeding
arising out of or relating to this Supplemental Indenture or the Additional
Notes.

      Section 4.  Counterparts.  The parties may sign any number of copies of
this Supplemental Indenture.  Each signed copy shall be an original, but all
of them together represent the same agreement.
<PAGE>
      Section 5. Ratification. Except as expressly amended hereby, each
provision of the Indenture shall remain in full force and effect and, as amended
hereby, the Indenture is in all respects agreed to, ratified, and confirmed by
each of the Issuers and the Trustee.

[Signatures on following page]
<PAGE>
      IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the date first above written.

                  CHARTER COMMUNICATIONS HOLDINGS, LLC



                  By:   /s/ Ralph G. Kelly
                        __________________________________________
                        Name:  Ralph G. Kelly
                        Title: Senior Vice President


                  CHARTER COMMUNICATIONS HOLDINGS CAPITAL CORPORATION


                  By:   /s/ Ralph G. Kelly
                        __________________________________________
                        Name:  Ralph G. Kelly
                        Title: Senior Vice President

                  BNY MIDWEST TRUST COMPANY, as Trustee


                  By:   /s/ Mary Callahan
                        __________________________________________
                        Name:  Mary Callahan
                        Title: Assistant Vice President