He was born in Olyphant, Pennsylvania of Ukrainian descent, and attended the University of Scranton. During World War II, he served in the Army in Europe; in the Battle of the Bulge he was wounded by shrapnel from an exploding shell, an injury which nearly cost him his sight. He earned both the Silver Star and Purple Heart during his service. After the war's end, he began umpiring amateur baseball in 1946, and returned briefly to college. He first worked in the minor leagues in 1947, reaching the American League seven years afterward.
He umpired in three ALCS, including the first one played (1969, 1972, 1973), serving as crew chief in 1969 and 1973, and in five World Series (1957, 1960, 1966, 1971, 1977), serving as the crew chief in 1971 (in which he called balls and strikes in the decisive Game 7) and 1977. He also worked in six All-Star Games: 1957, 1960 (both games), 1964, 1973 and 1978, calling balls and strikes in the second 1960 game and in 1973. After retiring from the field in 1978, he became an assistant league supervisor of umpires. Among his noteworthy games were Sandy Koufax's final game in the 1966 Series; "Ten Cent Beer Night" in Cleveland in 1974, where it was necessary for him to declare a forfeit due to constant fighting which spread onto the field and which saw Chylak hit over the head with a chair; and the first major league game ever played in Toronto in 1977, during a snowstorm at Exhibition Stadium, for which he was the home plate umpire.
As an assistant league supervisor, Chylak was in the umpires' dressing room at Comiskey Park on Disco Demolition Night, a July 12, 1979 doubleheader between the Detroit Tigers and Chicago White Sox. In between games of the doubleheader, when unruly fans began to blow up disco records on the field and rioted, Chylak told White Sox owner Bill Veeck that under no circumstances would the second game of the doubleheader be played. Veeck protested furiously, but Chylak's decision was upheld by American League president Lee MacPhail. The next day, MacPhail ordered the second game of the twinbill be forfeited to Detroit.
Chylak died of a heart attack at age 59 in Dunmore, Pennsylvania and is survived by his wife Sue, his sons Robert and William, and his grandsons and granddaughters Matt, Beth, William Jr, Sarah, Daniel, Joseph, and Nicholas. He was elected to the Baseball Hall of Fame in 1999.