Chambost began his footballing career with ES Veauche before being recruited to join the academy of Saint-Étienne, being part of the teams that won the under-13 and under-17 league championships.

[6] Chambost received his first professional appearance during a Coupe de France match on 24 January 2018 versus Troyes, coming on as a second half substitute.

[10][11] Chambost scored his first goal for Troyes in September, a second-half stoppage time winner to prevail 2–1 against Caen.

[12] On 20 June 2022, Chambost returned to Saint-Étienne, signing a two-year contract with the club and reuniting him once more with Laurent Batlles.

[24] Making his official debut for Columbus in the Leagues Cup against Sporting Kansas City, Chambost scored the final goal in a 4–0 win for his new side.