He was commissioned into the Bengal Artillery in 1858, which was later amalgamated into the Royal Artillery. He quickly caught the attention of Sir Frederick Roberts who predicted that Chapman would "make his mark". He was duly selected to fight in the British Expedition to Abyssinia between 1867 and 1868 as the commander of No. 5 Battery, 21st Brigade. He was present at the action of Arogee and at the fall of Magdala, working as aide-de-camp to Brigadier-General Petrie and being mentioned in dispatches for his services. Chapman was part of a mission to Yarkand in China in 1874. He served in the Second Anglo-Afghan War from 1878 to 1880, and was Sir Frederick Roberts' Chief of Staff during the march from Kabul to Kandahar.