Grandmaster
Byrne placed shared 4–7th at the 1957 U.S. Open Chess Championship in Cleveland with 9/12, a point behind joint winners Bobby Fischer and Arthur Bisguier. Byrne did not play in his first U.S. Chess Championship until age 30 in 1958–59, placing tied 9–10th with 4/11; the winner was Bobby Fischer. But Byrne improved dramatically the next year in the same event to place 2nd with 8/11, ahead of Reshevsky and Pal Benko, as Fischer won again.
In 1960, Byrne increased his serious play, winning the U.S. Open Chess Championship at St. Louis, and taking a silver medal on third board at the Olympiad in Leipzig. A poor result of 8–11th places in the U.S. Championship 1960–61, with only 4.5/11, was balanced by his fine tied 2nd–5th places at Mar del Plata 1961 with 11.5/15, behind winner Miguel Najdorf. On that same South American trip, he dominated a small but strong event at Santa Fe with 6.5/7, ahead of Miroslav Filip, Aleksandar Matanović, and Hector Rossetto. In the U.S. Championship of 1961–62, he tied for 2nd–3rd places on 7/11, half a point behind Larry Evans. He placed 6th in the U.S. Championship 1962–63 with 6/11, as Fischer won again. He again placed 6th in the U.S. Championship 1963–64 with 5.5/11, as Fischer won with a perfect score.
In 1964, Byrne's third-place finish at the Buenos Aires tournament (behind Paul Keres and World Champion Tigran Petrosian), with 11.5/17, made him an International Grandmaster. Byrne shared 2nd–3rd places in the U.S. Championship 1965–66 with 7.5/11; Fischer won again, but Byrne defeated Fischer in their individual game. He shared the 1966 U.S. Open title with Pal Benko at Seattle. He scored 4.5/11 for a shared 8–10th place, in the U.S. Championship 1966–67, with Fischer winning. Byrne qualified for his first Interzonal tournament, Sousse 1967, but scored just 7.5/22, far short of advancing.
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