Exhibit 2.1

AMENDMENT TO

AGREEMENT AND PLAN OF MERGER

BY AND AMONG

ARCH COAL, INC.,

ATLAS ACQUISITION CORP.

AND

INTERNATIONAL COAL GROUP, INC.

Dated as of May 26, 2011

THIS AMENDMENT TO THE AGREEMENT AND PLAN OF MERGER, dated as of May 26, 2011 (this “Amendment”), is entered into by and among Arch Coal, Inc., a Delaware corporation (“Parent”), Atlas Acquisition Corp., a Delaware corporation and wholly owned subsidiary of Parent (“Merger Sub”), and International Coal Group, Inc., a Delaware corporation (the “Company”). Capitalized terms used but not defined herein shall have the meanings ascribed to them in the Agreement and Plan of Merger, dated as of May 2, 2011, by and among Parent, Merger Sub and the Company (the “Merger Agreement”).

WHEREAS, the parties desire to amend the Merger Agreement so as to decrease the Company Termination Fee;

WHEREAS, the Board of Directors of the Company, and the respective Boards of Directors of Parent and Merger Sub have each approved this Amendment; and

WHEREAS, the parties have agreed to amend the Merger Agreement as provided in this Amendment.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto hereby agree as follows:

1. Amendment of Section 8.3. The reference to “$115 million” in Section 8.3(b) of the Merger Agreement is hereby amended to be “$105 million”.

2. References to the Merger Agreement. After giving effect to this Amendment, each reference in the Merger Agreement to “this Agreement”, “hereof”, “hereunder” or words of like import referring to the Merger Agreement shall refer to the Merger Agreement as amended by this Amendment and all references in the Company Disclosure Letter or the Parent Disclosure Letter to “the Agreement” and “the Merger Agreement” shall refer to the Merger Agreement as amended by this Amendment.

3. Construction. All references in the Merger Agreement, the Company Disclosure Letter and the Parent Disclosure Letter to “the date hereof” and “the date of this Agreement” shall refer to May 2, 2011.

4. Other Miscellaneous Terms. The provisions of Article IX (General Provisions) of the Merger Agreement shall apply mutatis mutandis to this Amendment, and to the Merger Agreement as modified by this Amendment, taken together as a single agreement, reflecting the terms therein as modified hereby.

5. No Further Amendment. Except as amended hereby, the Merger Agreement, shall remain in full force and effect. Nothing herein shall affect, modify or limit any waiver or consent granted by any party pursuant to the Merger Agreement. Each such waiver or consent remains in full force and effect.

[Signatures Appear on the Following Page]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be signed by their respective officers thereunto duly authorized, all as of the date first written above.