A machine tool for machining a workpiece clamped in the working space of the machine tool by means of a tool. The machine tool includes a machine bed, which has a chip collection region having at least one conveying channel open on the working space side for collecting chips that drop during the machining of the workpiece, and a conveying device for leading away chips that have dropped into the chip collection region in the at least one conveying channel. The conveying device has a stationary supporting shaft, which extends in the at least one conveying channel in the longitudinal direction of the conveying channel, wherein a spiral element is rotatably supported on the stationary supporting shaft, and wherein the conveying device also comprises a drive for driving the rotational motion of the spiral element about the stationary supporting shaft.