The patterning of graphene is useful in fabricating electronic devices, but existing methods do not allow control of the number of layers of graphene that are removed. We show that sputter-coating graphene and graphene-like materials with zinc and dissolving the latter with dilute acid removes one graphene layer and leaves the lower layers intact. The method works with the four different types of graphene and graphene-like materials: graphene oxide, chemically converted graphene, chemical vapor-deposited graphene, and micromechanically cleaved ("clear-tape") graphene. On the basis of our data, the top graphene layer is damaged by the sputtering process, and the acid treatment removes the damaged layer of carbon. When used with predesigned zinc patterns, this method can be viewed as lithography that etches the sample with single-atomic-layer resolution.