FIRST SUPPLEMENTAL INDENTURE

Exhibit 4.1

FIRST SUPPLEMENTAL INDENTURE

FIRST SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 15, 2014, among Cogent Communications Group, Inc., a Delaware corporation (the “Company”), Cogent Communications Holdings, Inc., a Delaware corporation (the “Guarantor”), and Wells Fargo Bank, National Association, as trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H

WHEREAS, the Company has heretofore executed and delivered to the Trustee an indenture (the “Indenture”), dated as of June 11, 2007 providing for the issuance of the Company’s 1.00% Convertible Senior Notes due 2027 (the “Notes”);

WHEREAS, on May 15, 2015, the Company merged with and into a wholly owned subsidiary of the Company (the “Merger”) and immediately following the Merger, the Company was a subsidiary of the Guarantor;

WHEREAS, the Guarantor desires to fully and unconditionally guarantee all obligations of the Company under the Notes and the Indenture on a senior basis on the terms and conditions set forth in the Indenture (the “Guarantee”); and

WHEREAS, pursuant to Section 10.01(d) of the Indenture, the Company and the Trustee are authorized to execute and deliver this Supplemental Indenture without notice to or consent of any Holder;

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company, the Guarantor and the Trustee mutually covenant and agree for the equal and ratable benefit of the Holders of the Notes as follows:

1.                                                              CAPITALIZED TERMS. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2.                                                              AGREEMENT TO GUARANTEE. The Guarantor hereby agrees to irrevocably fully and unconditionally provide the Guarantee subject to the conditions set forth in the Indenture.

3.                                                              NEW YORK LAW TO GOVERN. This Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

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.

5.                                                              EFFECT OF HEADINGS. The Section headings herein are for convenience only and shall not affect the construction hereof.

6.                                                              THE TRUSTEE. Except as otherwise expressly provided herein, no duties, responsibilities or liabilities are assumed or shall be construed to be assumed by the Trustee by reason of this Supplemental Indenture.  The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Guarantor and the Company.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed and attested, all as of the date first above written.

Signature Page to Cogent Communications Group, Inc.

Supplemental Indenture