Byrne was a competitor in Brooklyn chess coach and master John W. Collins chess club. Collins wrote about his students in the book My Seven Chess Prodigies, which features both Byrne brothers Donald and Robert and young Bobby Fischer.
Byrne won the U.S. Open Chess Championship in 1953 in Milwaukee and around that time he achieved the second-highest rating in the U.S., behind Reshevsky, against whom Byrne had a winning record. He was awarded the International Master title by FIDE (English: World Chess Federation) in 1962, and played for or captained five U.S. Chess Olympiad teams between 1962 and 1972. In 1972, he led a team representing Penn State University (the remainder of the team was alumni) to the US Amateur Team Championship in Philadelphia. The winning Penn State team consisted of Byrne, Dan Heisman, Steve Wexler, Bill Bickham, and Jim Joachim (alt.). Byrne's older brother, Grandmaster Robert Byrne, was also a leading player of that time.
Byrne was a great ambassador for American chess, seemingly on good terms with players from both sides of the Iron Curtain. At the 1966 Chess Olympiad in Havana, Cuba, Fischer, a member of the Worldwide Church of God, would not compete on Saturdays, and the tournament officials knew this, yet they scheduled his first game against a Soviet player on Saturday, leading to accusations and hot tempers by the U.S. and Soviet teams and the tournament officials. Byrne's diplomacy and communication skills and the respect that all the players had for his integrity were enough to get the game rescheduled with everyone saving face. The tournament proceeded without further incident. Host Fidel Castro gave Byrne a beautifully hand carved chess set as a thank you.
Byrne was repeatedly asked to be Captain by his teammates because of his interpersonal acumen and his generous, helpful nature. He routinely helped all the players analyze their games during adjournments and he repeatedly succeeded in getting the temperamental Fischer to "relax and play the game", as he would tell Bobby when stress threatened his continued participation in tournaments.
Byrne was very popular with the Penn State chess team players. In the late 1950s, Byrne contracted lupus, an auto-immune disease that led to the demise of his kidneys and made him allergic to the sun. He was known around campus for his very wide-brimmed brown Stetson hat. He would frequently tell stories about his chess exploits, often turning red from laughter. One story occurred in the 1956 Rosenwald tournament during the Game of the Century between Byrne and Bobby Fischer. Fischer was winning the game decisively and Byrne asked some of the other players if it would be a good "tip of the hat" to Fischer's superb play to let young Fischer play the game to a checkmate instead of Byrne resigning, which would normally happen between masters. When the other players agreed, Byrne played the game out until Fischer checkmated him. Byrne added "You have to remember, Bobby wasn't yet Bobby Fischer at that time", meaning that the then 13-year-old Fischer was "only" a master and not yet the 14-year-old wunderkind and top U.S. player he became the following year. Two other Byrne stories posted online: Fischer and the Border Patrol and The Hustler Gets Byrned.
As a player Byrne popularized the ...a5 line in the Yugoslav Attack in the Dragon Variation of the Sicilian Defense. Against 1.d4 he often preferred to play the Gruenfeld Defense. As White he preferred using the English Opening.
Born in New York City, Byrne was a professor of English. He taught at Penn State University from 1961 until his death, having been invited there to teach and to coach the varsity chess team. Before his time at Penn State, he was a professor at Valparaiso University in Indiana.
Geller–D. Byrne, Moscow 1955
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.f3 Nc6 8.Qd2 0-0 9.0-0-0 Be6 10.Kb1 Rc8 11.g4 Qa5 12.Nxe6 fxe6 13.Bc4 Nd8 14.Be2 Nd7 15.Bd4 Ne5 16.f4 Ndc6 17.Bxe5 dxe5 18.f5 Nd4 19.fxg6 hxg6 20.Rhf1 Rf4 21.g5 b5 22.Bd3 Rcf8 23.Qg2 b4 24.Ne2 Qc5 25.Qh3 Rf3 26.Rxf3 Rxf3 27.Qg4 Rxd3 28.Rc1 Rd1 29.c3 Rxc1+ 30.Kxc1 Nxe2+ 31.Qxe2 bxc3 32.Qg2 cxb2+ 33.Kxb2 Qb4+ 34.Kc2 a5 35.Qg4 Qc5+ 36.Kb3 Qb6+ 37.Kc3 a4 38.h4 Qd4+ 39.Kc2 Qf2+ 40.Kd3 Qxa2 41.h5 Qb3+ 42.Kd2 gxh5 0–1
In this game Byrne gives Samuel Reshevsky, who had clinched the tournament win the round before, his only defeat in a tournament best known for Bobby Fischer's "Game of the Century" win over Byrne:
D. Byrne-Reshevsky, Third Rosenwald Trophy 1956
1. d4 Nf6 2. c4 c5 3. d5 e6 4. Nc3 ed5 5. cd5 d6 6. e4 a6 7. a4 g6 8. Nf3 Bg4 9. Be2 Bf3 10. Bf3 Nbd7 11. O-O Bg7 12. Bf4 Qc7 13. Rc1 O-O 14. b4 Rfe8 15. a5 Qb8 16. bc5 Nc5 17. Na4 Na4 18. Qa4 Qd8 19. Qb4 Bf8 20. h3 Rb8 21. Rfe1 b6 22. ab6 Qb6 23. Qb6 Rb6 24. e5 de5 25. Be5 Ba3 26. Rcd1 Bb2 27. Bc7 Re1 28. Re1 Rb4 29. Rb1 Bc3 30. Rb4 Bb4 31. d6 Bc3 32. Bc6 Be5 33. g3 g5 34. Bd8 Kg7 35. d7 h5 36. Ba5 Nd7 37. Bd7 Kg6 38. Kg2 f5 39. Bc8 g4 40. h4 f4 1-0