Benko finished in first place (or tied for first place) in eight U.S. Open Chess Championships, a record. His titles were: 1961, 1964, 1965, 1966, 1967, 1969, 1974, 1975. He won the 1964 Canadian Open Chess Championship. He represented Hungary at the 1957 Student Olympiad in Reykjavík on , scoring 7½/12, and Hungary was fourth as a team. He had earlier played for the national Hungarian team at the Moscow 1956 Olympiad, on board three, scoring 10/15, and helping Hungary to team bronze. He moved to the United States, but it was not until 1962 that he appeared on the U.S. team. He would wind up on six teams in a row. At Varna 1962, Benko played board two, scored 8/12 for the silver medal on his board, and the U.S. finished fourth. At Tel Aviv 1964, he was again on board two, scored 9½/14, and the U.S. ended up sixth. At Havana 1966, Benko was on board three, scored 8/12, and the Americans won team silver. At Lugano 1968, he made 6/12 on board three, and the U.S. finished fourth. At Siegen 1970, Benko was on board four, scoring 8½/12, and the Americans again finished fourth. His last Olympiad was Skopje 1972, where he played on board three, made 9½/16, and the U.S. ended up ninth.