He was educated at Eton and King's College, Cambridge, where he graduated Bachelor of Arts (BA) in 1823, and Cambridge Master of Arts (MA Cantab) in 1826. He was made deacon in Ely in 1824 and ordained priest the next year in Chichester. He became a Fellow of King's College, one of the Masters of Eton, and Evening Lecturer at Windsor. In 1834, he was appointed to the Rectory of Dunton Wayletts, in Essex, the patronage of which was with King's College. On 7 November 1845, he was consecrated as the first Bishop of Colombo at St Peter's Church, Colombo, and received the degree of Doctor of Divinity (DD) from his University. In 1851, Chapman founded S. Thomas' College when it was in Mutwal before it relocated to its present site in Mount Lavinia He resigned the See of Colombo in 1861, and was elected a Fellow of Eton College, and was presented by the College in 1863 to the Rectory of Wootton Courtenay, Somerset. In 1868, he was made Prebendary of Warminster in Wells Cathedral. He was the author of occasional Charges, Sermons and Journals. During the mid-1860s, he undertook several bishop's duties (including ordinations of deacons/priests and consecrations of church buildings) in the Diocese of Exeter. In the late 1860s, when Robert Eden, Bishop of Bath and Wells, was ill, Chapman also assisted him as Coadjutor Bishop of Bath and Wells.
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- "Consecration of St Peter's Church, Newlyn, Penzance". Church Times (#174). 2 June 1866. p. 175. ISSN 0009-658X. Retrieved 26 December 2019 – via UK Press Online archives.
- "Church News". Church Times (#243). 28 September 1867. p. 337. ISSN 0009-658X. Retrieved 26 December 2019 – via UK Press Online archives.
- "The late Bishop Chapman". Church Times (#878). 21 November 1879. p. 731. ISSN 0009-658X. Retrieved 26 December 2019 – via UK Press Online archives.
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