Blenheim is a town in Marlboro County, South Carolina, United States. The population was 137 at the 2000 census. It is named for Blenheim Palace in Oxfordshire, England which itself is named for the Battle of Blenheim, a major English victory of the War of the Spanish Succession at what is now Blindheim, Germany. Blenheim apartments for rent comparison page shows most up to date rent information on Blenheim apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.