He attended the University of Georgia in Athens in 1820; however, he did not graduate from the school.

Chappell continued the study of law under the tutelage of Augustin Smith Clayton, passed the state bar exam, and became a practicing lawyer.

Upon the resignation of Representative-elect John B. Lamar, Chappell was elected as his replacement in the U.S. House of Representatives in 1843 and served in that position until 1845 when he did not seek re-election.

Chappell was subsequently elected to one more term as a state senator in 1845 and served as the president of that body.

Their four sons had prominent careers,[2] one as a president of normal schools and another as a state legislator.