The second U.S. warship to bear the name Drayton was a destroyer built by Bath Iron Works in Bath, Maine. Commissioned on 1 September 1936, the USS Drayton (DD-366) underwent final trials in Norfolk, Virginia, and then sailed for San Diego, where she arrived on 19 June 1937. Less than a month after arriving in Pacific waters, the Drayton was called on to take part in the futile search for the missing aviator Amelia Earhart. On 12 October 1939, the Drayton was transferred to Pearl Harbor, Hawaii.
When the Japanese attacked Hawaii on 7 December 1941, the Drayton was sailing with the USS Lexington (CV-2) as part of Task Force 12, which immediately began searching for the Japanese attackers before returning to Pearl Harbor on 13 December 1941. The Drayton next took part in escort duties to Christmas Island and then screened for the USS Enterprise (CV-6) group during a February attack on Bougainville.