 He was born in Westchester County, New York, the son of Peter DeLancey (1705–1770) and Elizabeth (née Colden) DeLancey.Among his siblings was brother Stephen DeLancey, also a member of the Nova Scotia Assembly, and sister Susan DeLancey, who was married to Thomas Henry Barclay, a lawyer who also became one of the United Empire Loyalists in Nova Scotia and served in the colony's government.His paternal grandparents were French immigrant Etienne DeLancey and Anne (née Van Cortlandt) DeLancey, herself the third child of Gertrude (née Schuyler) Van Cortlandt and Stephanus Van Cortlandt, the Chief Justice of the Province of New York.