Chevalier is a youth academy graduate of Lille.[2] He was third-choice goalkeeper of club behind Mike Maignan and Orestis Karnezis during their league title winning 2020–21 season. In July 2021, he joined Ligue 2 club Valenciennes on a season long loan deal.[3] He made his professional debut for the club on 18 September 2021 in a 1–1 draw against Pau.[4]
On 10 September 2022, Chevalier made his professional debut for his boyhood club with a strong performance against Marseille.[5] A few weeks later, on 9 October, he stopped a penalty kick and made decisive saves in Lille 1–0 home win over Derby du Nord rivals Lens. He was praised for his performance that earned him a rating of 8/10 in La Voix du Nord and a spot in L'Équipe's Team of the Week.[6][7] After the game, he told to Prime Video Sport pundit Thierry Henry that former Lille keeper Mike Maignan phoned him before the game to advise and encourage him.[8] In January 2023, Chevalier extended his contract with Lille until June 2027.[9]
On 2 October 2024, in his third season as Lille starting goalkeeper, he took part in the 1-0 home win against Real Madrid in the 2024–25 UEFA Champions League league phase. Being one of the best Lille players on the pitch, his performance was praised by various national and international media including L'Équipe which gave him a rare rating of 9/10 after the match.[10][11][12]