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Born in South Carolina on May 22, 1783, Crenshaw was the first graduate of the South Carolina College at Columbia, later renamed the University of South Carolina. He was elected to the South Carolina legislature in 1812, but moved to Cahawba, the first state capital of Alabama, in 1819. There, he was appointed a judge of the circuit court from 1821–1838, of the state supreme court from 1832, and as chancellor of the southern division of the state's courts. After his death in 1847, Crenshaw County, Alabama was named in his honor.