The invention relates to a clamping device (1) for fixing a tool in a machine tool, having a main body (2) that defines a clamping axis (X), said main body (2) comprising a machine interface (3), which has a fastening cone (4) and a ring flange (5) and is formed in the rear axial end region of the main body (2), and a clamping region (6), which defines a receptacle (7) for a tool shank and is formed in the front axial end region, located opposite the machine interface (3), of the main body (2), wherein the main body (2) has an external contour which is formed in a manner corresponding to that of a heat shrink chuck, wherein the receptacle (7) is surrounded annularly by a pressure chamber (9) that is chargeable with a hydraulic medium, wherein a thin wall (8) is provided between the receptacle (7) and the pressure chamber (9), said wall being elastically deformable inwards by an increase in the pressure in the pressure chamber (9), in order to fix, in a force-fitting manner, a tool shank inserted into the receptacle (7).