INCENTIVE PLAN OF CARRIZO OIL & GAS, INC. (As Amended and Restated Effective April 30, 2009) FIRST AMENDMENT

Exhibit 10.1

INCENTIVE PLAN

OF

CARRIZO OIL & GAS, INC.

(As Amended and Restated Effective April 30, 2009)

FIRST AMENDMENT

Carrizo Oil & Gas, Inc., a Texas corporation (the “Company”), having reserved the right under Section 13 of the Incentive Plan of Carrizo Oil & Gas, Inc., as amended and restated effective April 30, 2009 (the “Plan”), to amend the Plan for any purpose permitted by law, does hereby amend the Plan as set forth below.

The Plan is hereby amended, effective May 16, 2012, to increase the aggregate number of shares of the Company’s common stock available for issuance under the Plan by deleting the number “4,395,000” from Section 5 of the Plan and replacing said number with the number “7,245,000.”

IN WITNESS WHEREOF, this First Amendment has been executed effective as of May 16, 2012.