Denny was born in Carlisle, Pennsylvania, on March 11, 1761, the eldest son of William and Agnes Parker Denny. At the age of 13 he was entrusted to carry dispatches across the Allegheny Mountains by the commandant at Fort Pitt. He crossed alone often; to conceal his presence he hid in the woods at night. At one point he was chased into Fort Loudon by the Indians. He then entered into employment for his father's shop in Carlisle. Upon learning that a letter of the marque, a privateer ship, was to sail from Philadelphia for the West Indies, he shipped as a volunteer. He was promoted to command the quarter-deck for his gallantry in numerous sea fights.