Cheviot is a city in west-central Hamilton County, Ohio, United States. It is a suburb of Cincinnati. The population was 8,658 at the 2020 census…Cheviot is a city in west-central Hamilton County, Ohio, United States. It is a suburb of Cincinnati. The population was 8,658 at the 2020 census. In 1818, a Scottish immigrant named John Craig purchased a half section of 320 acres of Green Township from Elias Boudinot. He built an inn and tavern on the Harrison Pike. On March 21, 1818, Craig laid out a town which he named after the Cheviot Hills in southern Scotland. He sold lots and growth began.