Quigg, a 6'9 center out of St. Francis Prep in New York City, came to the University of North Carolina through coach Frank McGuire's "underground railroad" of players from New York to Chapel Hill. Quigg was a two-year starter at center in the 1955–56 and 1956–57 seasons. Quigg averaged 12.0 points and 9.0 rebounds per game as a sophomore, then 10.3 points and 8.6 rebounds per game as a junior. The Tar Heels went undefeated in his junior season and won the national championship. Quigg was instrumental in the championship game win, hitting the game-winning free throws and knocking down a pass from Kansas center Wilt Chamberlain in the closing seconds of the triple-overtime game.
Quigg was primed for a strong senior year in 1957–58, as the Tar Heels returned a strong nucleus from their championship team. However, he was injured in a preseason scrimmage and was out the entire season with a broken leg.
Even after missing his entire senior season, the New York Knicks spent a second round pick (#11 overall) on Quigg in the 1958 NBA Draft. Not fully healed, Quigg did not make the team. Instead, Joe Quigg went to dental school and became a dentist.
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