A tensioner for a traction drive includes a cylinder arranged in a housing at a distance to a housing wall to thereby define an interior space which contains hydraulic fluid. A piston is received in the cylinder for back-and-forth movement and bounds a pressure chamber containing hydraulic fluid. The piston has a cylinder-distal end which is operatively connected to a spring-biased tension roller supported on a traction member. Formed between the piston and the cylinder is a leakage gap, and a reservoir for hydraulic fluid is provided in an area of the leakage gap to prevent ingress of air into the pressure chamber, when the traction drive is at a rest.