Claremont is an incorporated town in Surry County, Virginia, United States. The population was 343 at the 2000 census. A granite marker stands as a memorial to the arrival of British settlers in the area. The town was incorporated in 1886, had a port on the James River, and gained railroad service as a terminus for a while before being abandoned. Claremont was home to the Temperance, Industrial, and Collegiate Institute, a school for African Americans founded by a former slave. The area includes a historical marker commemorating the institution.