A chain tensioner for use with a chain of a vehicle engine, includes a housing and a plunger slidably mounted in a cylinder chamber formed in the housing. The plunger is biased outwardly by a return spring mounted in a pressure chamber defined in the cylinder chamber by the plunger. A check valve is provided in the cylinder chamber to prevent backflow of hydraulic oil in the pressure chamber. A relief valve, provided in the plunger, opens above a relief pressure, thereby discharging hydraulic oil in the pressure chamber. An oil leakage clearance is defined between the plunger and the inner wall of the cylinder chamber. The relief pressure and the oil leakage clearance dimension are determined such that the tension in the chain is kept at such a level that vibrations of the chain are minimum at any temperature of hydraulic oil and at any engine revolution speed.