Rivals is a small unincorporated rural community on the banks of Brashear's Creek in Spencer County, Kentucky, United States. At on…Rivals is a small unincorporated rural community on the banks of Brashear's Creek in Spencer County, Kentucky, United States. At one time it had a general store started by Matthias Carland's family who settled the land beginning in 1796. Also a post office and a grist mill, started by Peter Van Dyke and his sons, which began operating in 1789. These businesses have been gone for many years, though the building that served as the store and post office still stands as a storage building for a home. It is located approximately 5 miles north-northeast of Taylorsville.