The sitter was the eldest son of Richard Chapman of Tainfield House, nr. Taunton, Somerset, and Mary, daughter of Stephen Remnant. He attended the Royal Military Academy at Woolwich, and was commissioned Second Lieutenant in the Royal Engineers in 1793, and Lieutenant in 1796. By 1805 he had been promoted to captain, and served in the expedition to Copenhagen in 1807. In 1809 he joined the army in Portugal where his skills were quickly noted by Sir Arthur Wellesley, preparing for the defence of Lisbon during the Talavera campaign. By 1810 he was appointed to the office of Secretary to the Master-General, and was secured a promotion to the rank of Major by Wellesley in 1812, and in 1813 to Lieutenant-Colonel in the Royal Engineers.
Chapman was promoted to Colonel in 1825, and was Civil Secretary at Gibraltar from 1825-1831. In 1831 he was knighted, and until 1839 was Governor of Bermuda where his most important duty was the emancipation of slaves there in 1834. In 1837 he was promoted to Major-General, and in 1846, to Lieutenant-General, becoming Colonel-Commandment of the Royal Engineers in 1850.