Dexter is a town in Penobscot County, Maine, United States. It is part of the Bangor, Maine metropolitan statistical area. Dexter Regional High School, which serves Dexter as well as other nearby small towns, is located in the town. Dexter was settled beginning in 1801 by Ebenezer Small, David Smith, and others from New Hampshire, and was originally called Elkinstown. When incorporated as a town in 1816, it named itself after Samuel Dexter, who was then running for governor of Massachusetts (of which Maine was a territory). The town of Brooks, Maine in nearby Waldo County, was incorporated the same year and named for the opposing candidate, John Brooks. Brooks won the election. The town of Dexter, however, achieved the greater prosperity.