The invention relates to a clamping device (1) for clamping a machine element (3) which rotates around a rotational axis (9), especially a tool holder for a boring tool, milling tool, grinding tool or the like. The inventive clamping device comprises a base body unit (11) having a receiving opening (21) which is centrically arranged in relation to the rotational axis (9). A coupling shaft (5) of the machine element (3) can be axially inserted with a front end into said receiving opening. The clamping device also has a collet chuck (23) which is arranged in the receiving opening (21), and has a jaw actuating unit (25) which is provided for actuating the collet chuck (23), is guided on the base body unit (11), and which can be axially displaced in relation thereto. The aim of the invention is to attain a degree level of reproducibility of the out-of-balance measurements when using said clamping device (1) in a balancing machine. To this end, the jaw actuating unit (25) is axially guided on the base body unit (11) by a roll body arrangement (35) whose roll bodies (39) roll on roll surfaces (41, 43) of the base body unit (11) and of the jaw actuating unit (25). The roll body arrangement (35) is preferably formed by a ball cage unit whose balls (39) are fitted with pretension between the base body unit (11) and the jaw actuating unit (25).