We present high-resolution measurements on the closure domain pattern of Co(0001) obtained with spin-polarized scanning tunneling microscopy. Besides the well-established wide surface domain walls we find ultra sharp sections of the wall. The width of these walls is only 1.1 nm, an order of magnitude less than previously observed in bulk Co. The ultra sharp domain walls are explained on the basis of a micromagnetic model taking into account the competition of exchange energy and magnetic anisotropy.