We report on DNA translocations through nanopores created in graphene membranes. Devices consist of 1-5 nm thick graphene membranes with electron-beam sculpted nanopores from 5 to 10 nm in diameter. Due to the thin nature of the graphene membranes, we observe larger blocked currents than for traditional solid-state nanopores. However, ionic current noise levels are several orders of magnitude larger than those for silicon nitride nanopores. These fluctuations are reduced with the atomic-layer deposition of 5 nm of titanium dioxide over the device. Unlike traditional solid-state nanopore materials that are insulating, graphene is an excellent electrical conductor. Use of graphene as a membrane material opens the door to a new class of nanopore devices in which electronic sensing and control are performed directly at the pore.