A tapping tool for producing a threaded bore having an internal thread in a workpiece. The tapping tool has a main cutting edge on its drill tip and a thread profile trailing in a tapping direction. The method has a tapping stroke in which the tapping tool is driven into the workpiece at a tapping feed rate in the tapping direction and at a tapping speed synchronized therewith and the main cutting edge of the tool produces a core hole bore and the tool thread profile forms an internal thread on the inner wall of the core hole bore. Chips are produced in the tapping stroke, which are conveyed out of the threaded bore in a chip removal direction opposite to the tapping direction and collide with thread flanks of the internal thread facing toward the chips to be removed.