Army Combat Action Badge Eligibility Act This bill authorizes the Department of the Army to award the Army Combat Action Badge to a person who (1) participated as a member of the Army in combat during which the person was personally engaged with the enemy at any time from December 7, 1941, to September 18, 2001, and (2) has not been recognized previously for such participation. The Army may make arrangements with suppliers of the badge so that eligible persons may procure it directly from suppliers, thereby substantially reducing or eliminating administrative costs for carrying out this bill.