The daughter of John Chancellor and Mary Jolliffe, a daughter of Lord Hylton, Chancellor was brought up in Somerset and educated at St Mary's School, Shaftesbury, a Roman Catholic boarding school for girls in Dorset, but left at sixteen to live in London, later describing her early years there as "quite wild". She became the partner of the poet Jock Scot (1952–2016), and in her early twenties had a daughter, Poppy, whilst still studying at the London Academy of Music and Dramatic Art. She separated from Scot a few years later. She got her first acting role on television playing Mercedes Page in Jupiter Moon, a BSkyB soap, then came a commercial for Boddingtons beer and a part in the film Four Weddings and a Funeral (1994), playing "Duckface" opposite Hugh Grant.