Chapman was born in 1910 in Alcester, Warwickshire. He came up to Pembroke College in 1929 from Marlborough, and studied Natural Sciences. In 1931 he was designated Smart-Scrivener Scholar and was awarded the Blackburne-Daniell Prize. Chapman completed his degree in 1932 and was a designated Foundress Scholar. He also received a grant for research and received a Tripos Prize the same year. In 1933 he was appointed to the Frank Smart Studentship at Gonville and Caius College, and from 1935-36 was a Henry Fellow at Harvard. He worked as a Professor of Botany for 35 years at the University of Auckland. For his academic work, primarily on algology, mangroves, and coastal conservation, he was appointed an Officer of the Order of the British Empire in 1974, and in 1977 was awarded the Queen Elizabeth II Silver Jubilee Medal. He died in Auckland in 1980.