The tensioning device includes a guide rod (8) which has an outer contour for guiding a cutting chain around it. A chain wheel (7) drives the cutting chain, and the chain saw casing (4) supports the guide rod, chain wheel and the drive for it. A leaf spring (13) is fitted between the guide rod and saw casing. It bears against the guide rod in the longitudinal direction to tension it away from the chain wheel and establishes a desired tensioning of the cutting chain.