Undrafted, Chelios made his professional debut following his senior year in 2013–14, playing alongside brother Dean with the Toledo Walleye of the ECHL before joining the Chicago Wolves of the AHL.

[3] After posting a breakout season in the 2015–16 campaign in scoring 31 points in 73 games with the Charlotte Checkers, Chelios was signed to his first NHL contract with parent affiliate, the Carolina Hurricanes on April 22, 2016.

[6] On March 29, 2019, the Red Wings recalled Chelios from the Grand Rapids Griffins under emergency conditions.

Chelios embarked on a career abroad as an impending free agent, agreeing to a two-year contract with Chinese-based KHL club, Kunlun Red Star, on May 23, 2019.

While the Olympic Charter stipulates that any athlete competing in the Games must be a national of the country of the NOC which is entering such competitor, the IOC Executive Board has the authority to make certain exceptions of a "general or individual nature", though it is unclear whether this was the case.