He was selected by the Atlanta Thrashers in the 4th round (120th overall) of the 2009 NHL Entry Draft, and made his professional debut in the American Hockey League with the Chicago Wolves during the 2009–10 season.

[5] On July 23, 2014, Chiarot signed a two-way deal, worth $600,000 with the Jets, after a strong campaign with the St. John's IceCaps of the American Hockey League.

While playing with the Canadiens over the course of the contract, Chiarot assumed an increasingly prominent role in their defense corps, notably participating in the team's deep run to the 2021 Stanley Cup Finals, where they lost to the Tampa Bay Lightning.

"[13] Entering the final season of his contract, he became the subject of increasing speculation that he would be traded before the deadline in order to secure the Canadiens more picks in the 2022 NHL Entry Draft.

[15] On March 15, coach Martin St. Louis announced that he would sit out the remaining games in advance of the trade deadline to avoid injury.

[17] Following the trade, Chiarot remained in Montreal rather than joining the team on the road, and made his debut with the club on March 24 in a game against the Canadiens.