A tool spindle having a spindle shaft rotationally-drivable about a spindle axis, a clamping system for the automatic chucking and unchucking of a tool, wherein the clamping system comprises a movement device enabling at least one movable and/or deformable clamping body of the clamping system to be transferred from a first position into a second position by execution of a movement of a part of the movement device in relation to the spindle shaft, wherein the tool is chucked on the tool spindle in the first position and the tool can be removed from the tool spindle in the second position, wherein it comprises a balancing system, which is integrated into the tool spindle so that it rotates jointly with the rotationally-drivable spindle shaft, which is arranged coaxially in relation to the spindle axis, and which is mounted so it is axially movable.