The invention relates to a cooling device for a chip, in particular a processor, embodied with a number of projections or fins standing essentially normal on a base surface facing away from the chip and which may be fixed to the chip by the base surface on the side thereof facing the chip. The base surface is embodied with a number of steps or ribs, which in particular form a number of through channels on arranging the base surface on the chip, whereby the channels are embodied in the base surface in a non-linear but rather in particular in a bent manner, which permits the production of a small cooling device with an appropriate cooling capacity.