A mechanical power-transmission system with chain including a mechanical tightener acting on a branch of the chain and having in turn a base, a tightening shoe in dragging contact with the chain and a sliding wedge under the thrust of a first spring in an irreversible manner between the base and the shoe to cause progressive withdrawal of the base and the shoe in the tightening direction of the chain so that between the wedge and the shoe there is an elastic thrust member for thrusting the shoe in the tightening direction.