Exhibit 5.1

OPINION OF DAVIS POLK & WARDWELL LLP

September 28, 2009

GHL Acquisition Corp.

300 Park Avenue, 23rd Floor

New York, NY 10022

Ladies and Gentlemen:

We have acted as counsel for GHL Acquisition Corp., a Delaware company (the “Company”) in connection with the Registration Statement on Form S-3 (File No. 333-159673) and Amendments Nos. 1 and 2 thereto (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Securities Act”) for the purpose of registering the sale of 18,400,000 shares of its common stock, par value $0.001 per share, which includes 2,400,000 shares subject to the Underwriters’ option to purchase additional shares (the “Common Stock”).

We, as your counsel, have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

Based upon the foregoing, we are of the opinion that when the shares of Common Stock are issued and delivered to and paid for by the Underwriters pursuant to the Underwriting Agreement dated September 23, 2009 among the Company, Iridium Holdings LLC, Raymond James & Associates, Inc., RBC Capital Markets Corporation and Stifel, Nicolaus & Company, Incorporated, as representatives of the several Underwriters named in Schedule I thereto, such shares of Common Stock will be validly issued, fully paid and non-assessable.

We are members of the Bar of the State of New York and the foregoing opinion is limited to the laws of the State of New York and the General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement referred to above and further consent to the reference to our name under the caption “Validity of the Securities” in the prospectus, which is a part of the Registration Statement.  In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

This opinion is rendered solely to you in connection with the above matter.  This opinion may not be relied upon by you for any other purpose or relied upon by or furnished to any other person without our prior written consent.

Very truly yours,

/s/ Davis Polk & Wardwell LLP