2005-06: Cheverie played for the Nanaimo Clippers of the BCHL. He appeared in 46 regular season games and was 23-9-0 and posted a 2.54 GAA with a .903 save percentage and 4 shutouts. Cheverie had a rough playoffs, going 1-3 in four games as the Clippers were eliminated in the first round. Cheverie posted a 3.34 GAA and .878 save percentage.
2006-07: Cheverie played in 34 with Nanaimo and was 21-9-2 with three shutouts, a 3.10 GAA and .875 save percentage. Appeared in five playoff games and was 2-1 with a 3.34 GAA and .888 save percentage. He committed to the University of Denver.
2007-08: With senior Peter Mannino starting 40 games, Cheverie saw little action in his freshman season at Denver. He started one game, a win over Bemidji State in January, and appeared in five games. In 141 minutes of action, he posted a 1.70 GAA and .917 save percentage. Denver, after finishing third in the WCHA regular season, captured the league's tournament championship with a 2-1 win over Minnesota.
2008-09: Cheverie took over as the Pioneers starter in his second season with Denver. Cheverie was 23-12-5 with four shutouts with a 2.34 GAA and .921 save percentage for Denver as the Pioneers finished second in the wCHA regular season. He was at his best in the WCHA championship game, stopping 42 shots in a 3-0 shutout win over high-powered Wisconsin. Cheverie was named to the WCHA Second All-Star Team.
2009-10: Cheverie was one of the top goaltenders in college hockey as a junior leading the Pioneers, the NCAA's top-ranked team for much of the year, to a WCHA regular season title. Cheverie finished with a record of 24-6-3 with six shutouts and a 2.08 GAA and .932 and was named the WCHA's Top Goalie and Player of the Year. Cheverie signed an entry level contract with Florida in April and will forego his senior season at Denver.
2010-11: Cheverie made his AHL debut in February 2011 and finished his first pro season with Rochester after playing 30 games for the ECHL's Cincinnati Cyclones prior to being promoted. Playing for a Rochester team that struggled offensively and finished last in the North Division, Cheverie appeared in 15 games and was 2-8 with one overtime loss and had a 3.91 GAA and .888 save percentage. In 30 games with the Cyclones he was 13-14 with five of the losses coming in overtime. Cheverie had three shutouts and a 3.11 GAA and .896 save percentage.
Cheverie uses his large frame to cover the net effectively. He is athletic and has above average quickness with good reflexes. Cheverie likes to challenge shooters and takes an aggressive approach to goaltending. Cheverie was very successful during his college career by playing a controlled, deliberate style emphasizing positioning.
Cheverie will probably start the season at the ECHL level, depending on the status of Markstrom’s recovery. If Markstrom struggles to recover from knee surgery, Cheverie could find himself splitting time with Tyler Plante in San Antonio. He has the size and athleticism to become a starter in the NHL, but projects as more of a quality, journeyman backup who can carry the load short-term if necessary.