Domestic Offshore Energy Security Act

Domestic Offshore Energy Security Act - Authorizes United States persons to: (1) engage in any transaction necessary for exploration and extraction of hydrocarbon resources from any portion of any foreign exclusive economic zone contiguous to the Exclusive Economic Zone of the United States; and (2) export without license authority all equipment necessary for such activity.

Amends the Trade Sanctions Reform and Export Enhancement Act of 2000 to direct the Secretary of the Treasury to grant general license authority for travel-related expenditures to, from, or within Cuba by persons engaging in hydrocarbon exploration and extraction in any part of a foreign maritime Exclusive Economic Zone contiguous to the U.S. Exclusive Economic Zone.

Amends the Gulf of Mexico Energy Security Act of 2006 to: (1) repeal the oil and gas leasing moratorium governing any area east of the Military Mission Line; and (2) decrease from within 125 to within 45 miles of the Florida coastline the moratorium upon oil and gas leasing in the Eastern and Central Planning Area.

Instructs the Secretary of the Interior to promulgate regulations that establish environmental safeguards for exploration and production of oil and natural gas on the outer Continental Shelf.

Authorizes the Secretary of the Interior to conduct an oil and natural gas inventory beneath the waters of the outer Continental Shelf off the coasts of Virginia, North Carolina, South Carolina, or Georgia, but only upon request of the affected state governor.

Amends the Energy Policy Act of 2005 regarding the program of grants to oil and gas producers to carry out projects to inject carbon dioxide for the purpose of enhancing oil or natural gas recovery while increasing the sequestration of carbon dioxide. Directs the Secretary of Energy to grant priority consideration to applications that, together with meeting other requirements, are carried out in geologically challenging fields.