With a 3-4-0 record, the Senators currently sit 22nd in the NHL and 7th in the Atlantic Division.
The 26 year-old Chabot has yet to play a full 82 game season in his career, with 71 games in the 2019-20 campaign being his highest number of games played.
Brannstrom took a hit in Thursday's game against the New York Islanders and was taken to the hospital where he was responsive.
Being in the NHL's Atlantic Division, the Senators will not have an easy feat climbing up the standings into a possible wild card spot, and being without three of their blueliners puts them in a rough spot early in the season.
Jakob Chychrun and Jake Sanderson are expected to get a major increase in ice time as the Senators look to turn their season around.