Frank Chapot competed in Olympic show jumping six times, winning two silver medals in the team event, and having a highest individual placing of fourth in 1968. He was one of the first American Olympians to compete in six Olympic Games. At the Pan American Games Chapot won two golds in team jumping, in 1959 with Hugh Wiley, Bill Steinkraus, and George Morris and 1963 with Mary Mairs, Kathy Kusner, and Steinkraus, and two silver medals, one in the individual show jumping event in 1959 and one with the jumping team in 1967, which consisted of the same members as four years before. In 1966 Chapot placed second in the European Show Jumping championship to become the first American medalist in this event.
In 1965 Chapot, a Penn and Wharton graduate, married Mary Mairs, twice his Olympic teammate, and they later farmed in New Jersey. Chapot became the US Equestrian Team (USET) chef d’équipe, a position he held until retirement in 2005. He served the USET as vice-president for show jumping and worked as a course designer and judge. He was a founding member of the Show Jumping Hall of Fame Board of Directors and served on the Board of Directors of the American Grandprix Association (AGA). He also rode timber races, notably at the Maryland Hunt Cup. Chapot was inducted into the Show Jumping Hall of Fame in 1994.