Hunter was born on 19 February 1965 in Dunedin, New Zealand. He is the son of John Alexander Hunter and his wife Alice Mary Hunter. He and his family moved to Northern Ireland in 1969. He was educated at Portstewart Primary School and the Coleraine Academical Institution, an all-boys grammar school in Coleraine, County Londonderry. He studied Natural Sciences and then chemistry at the University of Cambridge. He graduated with a Bachelor of Arts (BA) degree in 1986, this was later promoted to Master of Arts (MA Cantab) as per tradition, and with a Doctor of Philosophy (PhD) degree in 1989.