Dunlap was launched 18 April 1936 by United Shipyards, Inc., New York, New York; sponsored by Mrs. Katherine Wood Dunlap, widow of Brigadier General Dunlap; and commissioned 12 June 1937, Commander A. E. Schrader in command.
Dunlap operated along the east coast on training duty, and in June 1938 served as escort at Philadelphia, Pennsylvania for the MS Kungsholm, carrying the Crown Prince of Sweden.