Chabot started off in Midget AAA in Quebec with Trois-Rivieres Selects, playing in 34 games with a 25-9-0 record before moving onto the QMJHL in the 1986-87 season with the Drummondville Voltigeurs, playing in 62 games that season with a 31-30-0 record, then 2-6 in eight playoff appearances. The 1987-88 was a better on while in Drummondville, with Chabot going 27-24-4 in 58 games, but a 10-6 record in 16 playoff games; though they lost to the Hull Olympiques in the Finals. Chabot also went 0-3 in the three Memorial Cup games that Drummondville played in.
As an "over-aged" player, Drummondville waived Chabot and he landed in the WHL for the 1988-89 season, playing for the Moose Jaw Warriors, but ending his season there with the Prince Albert Raiders.
As his junior career ended, Chabot went to the IHL to play with the Fort Wayne Komets for the 1989-90 season, playing in 23 games with a 6-13-3 record. However, midway through the season, Chabot signed with the Montreal Canadiens, where they would place him in the AHL with the Sherbrooke Canadiens, going 1-1-0 in two games.
Chabot was back in the AHL for the bulk of the 1990-91 season, playing with the Fredericton Canadiens, going 9-15-5 in 35 games; also getting called up by Montreal for three games, going 0-0-1 in those appearances. Chabot was back with Fredericton in the 1991-92 season, compiling a 17-9-4 record in 30 games; then a 3-4 record in seven playoff games. Chabot also spent 24 games in the ECHL with the Winston-Salem Thunderbirds, finishing with a 15-7-2 record. The 1992-93 season had Chabot play in 45 games for Fredericton and finishing with a 22-17-4 record, then a 1-3 playoff record. Chabot racked up the travel miles for himself in the 1993-94 season, playing for Fredericton for three games (0-1-1), then moving to the IHL's Las Vegas Thunder for two games (1-1-0) and Montreal for one (0-1-0).
Chabot was dealt to the Philadelphia Flyers for cash, playing in four games for the Flyers and going 0-1-1. He would spent the bulk of his time with the AHL's Hershey Bears, finishing with a 13-5-6 record in 28 games, then 7-4 in 11 playoff games. Chabot was awarded the Baz Bastien Award for AHL's Outstanding Goaltender.
Chabot signed with the Florida Panthers before the 1994-95 season, but he would play in the IHL with the Cincinnati Cyclones, posting a 25-12-7 record in 48 games, then 3-2 in five playoff games. Back in Cincinnati for the 1995-96 season, Chabot had a 23-9-4 record in his 38 games, then going 9-5 in 14 playoff games. The 1996-97 season saw Chabot play with the Houston Aeros of the IHL, going 39-26-7 in 72 games before going 8-5 in 13 playoff games. That season, Chabot was awarded the James Gatschene Memorial Trophy for IHL MVP.
The Los Angeles Kings signed Chabot for the 1997-98 season, but only played 12 games for them, finishing with a 3-3-2 record. Chabot spent the rest of the year with Houston again, finishing with a 12-7-2 record and 1-3 playoff record that season.
The summer of 1998 was confusing for Chabot-- who was claimed by the Nashville Predators in the Expansion Draft; then picked off waivers by the Kings again, finally picked up off waivers again by the Montreal Canadiens. Chabot spent 11 games with Montreal in the 1998-99 season, finishing with a 1-3-0 record in Montreal, but most of his time would be back in Houston; going 16-4-1 in 22 games there. In the 1999-2000 season, Chabot was back in Houston, playing in 62 games and finished with a 36-19-7 record and going 6-5 in 11 playoff games. Chabot racked up the awards, winning the Gatschene Trophy for MVP again, sharing with Nikolai Khabibulin, while also winning the James Norris Trophy for fewest goals against. Chabot was back in Houston in the 2000-01 season, finishing with a 23-16-5 in 47 games, then going 3-4 in the playoffs.
Starting in the 2001-02 season, Chabot moved it over season-- playing for the Nurnberg Ice Tigers from 2001 until 2004. In the 2004-05 season, Chabot moved to Austria to play with the Vienna Capitals before going back to Germany for the 2005-06 season, this time with Alder Mannheim. After that season, Chabot hung up the pads for good.
Chabot would go far from hockey, as he stayed in Europe to be the goaltending coach for AIK Stockholm (Sweden) in 2006, then over to Germany to coach for the Berlin Ice Bears, before returning to North America to be the goaltending coach for the Edmonton Oilers. Chabot has also had ties with Hockey Canada's World Junior Program.
While he did get bounced around a lot and mostly made relief duties, the time he spent in the minors allowed him to garner knowledge to pass around to the youth players coming up through the ranks and now onto the new generation of goalies in Edmonton.