Afton is an unincorporated community in Greene County, Tennessee. It is believed that the community's name comes from Robert Burns's song "Sweet Afton", about the River Afton in Scotland. Its ZIP code is 37616.Some of Afton has been annexed by the town of Greeneville and the city of Tusculum.Chuckey-Doak High School and Chuckey-Doak Middle School are the only schools in Afton.Afton has its own post office and zip code. The post office is located at 432 Afton Road, Afton, Tennessee 37616.