David Chapman was a member of the class of 1897 but did not earn a degree. He was quarterback of the 1894 and 1895 club intercollegiate football team (the athletic association abandoned football in 1894, and UT played as a club sport in 1894 and 1895). He joined his father’s company, Chapman, White, Lyons Company, a wholesale drug company, in 1900 after service in the Spanish American War as a lieutenant of the Third Tennessee Infantry. Following the death of his father, he purchased the interest in the firm of W. L. Lyons, who retired from the firm, and in 1907 he reorganized the company and changed its name to Chapman Drug Company.
Chapman was an organizer and first president of the Knoxville Rotary Club, president of the Knoxville Board of Trade, a member of the Board of Commerce, and director and stockholder in the City National Bank. He became a colonel in the Fifth Tennessee Regiment (later renamed to Fourth Tennessee Regiment) before resigning on November 20, 1918.
A longtime member of the Appalachian Club at Elkmont, Tennessee, he was instrumental in establishing the Great Smoky Mountains National Park and was the first chair of the Great Smoky Mountains National Park Commission, established by the Tennessee Legislature in 1927. He was also the chairman of the Great Smoky Mountains Conservation Association from August 1931 until his death in 1944. In 1931 a 6,340-foot peak within the Smokies was named for him. Chapman Highway (US 441), leading from Knoxville to the Smokies, is also named for him.