The hollow plunger of a hydraulic tensioner for an engine timing chain protrudes from a tensioner housing in an oblique downward direction. An inner sleeve fixed to the housing slidably protrudes into the interior of the plunger, and has a ball check valve at its protruding end. Oil is supplied though the sleeve and the check valve to a high pressure oil chamber formed inside the plunger, and flows outward through a two-part leakage path formed by a gap between the sleeve and the interior of the plunger and a gap between the exterior of the plunger and an interior wall of a plunger-accommodating hole in the housing. Any air that enters the tensioner accumulates in a region surrounding the upper end of the sleeve, rather than in the high oil pressure chamber inside the plunger.