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.