Allan Chapman has been based at Oxford University for most of his career, as a member of the Faculty of History, based at Wadham College. He is an accomplished lecturer and public speaker (including as visiting professor at Gresham College in London). In January 1994, he delivered the Royal Society history of science Wilkins Lecture, on the subject of Edmund Halley.
He is also a television presenter, notably Gods in the Sky, covering astronomical religion in early civilisations, and Great Scientists, presenting the lives of five of the greatest thinkers. Not averse to other forms of television, he also participated in the TV quiz University Challenge – The Professionals as part of the Royal Astronomical Society team, broadcast in June–July 2006. He is a Fellow of the Royal Astronomical Society, and took over the presidency of the Herschel Society after the death of Sir Patrick Moore, the previous holder of the post.
