Gillies, 27, has appeared in four AHL games overall this season, including three with Providence and one with Lehigh Valley.
The 6-foot-6, 223-pound goaltender has posted a 3-1-0 record this season with a 1.76 goals-against average and a .939 save percentage.
The Concord, New Hampshire native has made 12 career NHL appearances, logging a 4-5-1 record with a 2.71 goals-against average and a .903 save percentage.