What is proposed is a hydraulic lash adjuster (1), for example for a valve train of an internal combustion engine. The lash adjuster (1) comprises a hollow cylindrical housing (2) that is inter-inserted with an axially relatively displaceable pressure piston (3). A high pressure chamber (6) for hydraulic medium extends between opposing front ends (4, 5) of the pressure piston (3) and the housing (2). The high pressure chamber (6) can be supplied, via a one-way valve (8) arranged on the front end (4) and opening towards the high pressure chamber (6) with hydraulic medium out of a reservoir (9). A leak gap (12) for the hydraulic medium is formed between an outer peripheral surface (10) of the pressure piston (3) and a bore (11) of the housing (2). In its portion adjoining the front end (5) of the housing (2), the bore (11) of the housing (2) merges into an annular enlargement (15). According to the invention, the front end (4) of the pressure piston (3) comprises in its transition region to the outer peripheral surface (10), a chamfer (16) whose height (HF) is equal to or larger than a height (HR) of the annular enlargement (15). In this way, it is effectively prevented that undesired particles situated in the high pressure chamber (6) get deposited on the outer peripheral surface (10) of the pressure piston (3) in the sunk state thereof, and penetrate into the leak gap (12) during the subsequent adjusting operation with the danger of a clamping of the pressure piston (3).