Born on Little River, near Columbia, Fairfield District, South Carolina, where the family was on a visit, Chappell was, as an infant, taken by his parents to their home on the Congaree River, Richland District, South Carolina.

He was admitted to the bar in 1805 and commenced practice in Columbia, South Carolina.

He served as chairman of the Committee on Pensions and Revolutionary Claims (Thirteenth and Fourteenth Congresses).

He served as director of the Columbia branch of the State Bank of South Carolina 1830–1858.

He was interred in First Baptist Church Cemetery, Columbia, South Carolina.