The interaction of cell and organelle membranes (lipid bilayers) with nanoelectronics can enable new technologies to sense and measure electrophysiology in qualitatively new ways. To date, a variety of sensing devices have been demonstrated to measure membrane currents through macroscopic numbers of ion channels. However, nanoelectronic based sensing of single ion channel currents has been a challenge. Here, we report graphene-based field-effect transistors combined with supported lipid bilayers as a platform for measuring, for the first time, individual ion channel activity. We show that the supported lipid bilayers uniformly coat the single layer graphene surface, acting as a biomimetic barrier that insulates (both electrically and chemically) the graphene from the electrolyte environment. Upon introduction of pore-forming membrane proteins such as alamethicin and gramicidin A, current pulses are observed through the lipid bilayers from the graphene to the electrolyte, which charge the quantum capacitance of the graphene. This approach combines nanotechnology with electrophysiology to demonstrate qualitatively new ways of measuring ion channel currents.