Gillies played collegiate hockey with the Providence Friars in the NCAA Men's Division I Hockey East conference. In his freshman year, Gillies's outstanding play was rewarded with a selection to the 2012–13 All-Hockey East First Team. He was the starting goaltender for the United States at the 2014 World Juniors and played nearly every minute of the tournament, but failed to medal. During his junior season, Gillies led the Friars to the NCAA title, being chosen as the Frozen Four Most Outstanding Player.