Coulomb drag is a process whereby the repulsive interactions between electrons in spatially separated conductors enable a current flowing in one of the conductors to induce a voltage drop in the other(1-3). If the second conductor is part of a closed circuit, a net current will flow in that circuit. The drag current is typically much smaller than the drive current owing to the heavy screening of the Coulomb interaction. There are, however, rare situations in which strong electronic correlations exist between the two conductors. For example, double quantum well systems can support exciton condensates, which consist of electrons in one well tightly bound to holes in the other(4-6). 'Perfect' drag is therefore expected; a steady transport current of electrons driven through one quantum well should be accompanied by an equal current of holes in the other(7). Here we demonstrate this effect, taking care to ensure that the electron-hole pairs dominate the transport and that tunnelling of charge between the quantum wells, which can readily compromise drag measurements, is negligible. We note that, from an electrical engineering perspective, perfect Coulomb drag is analogous to an electrical transformer that functions at zero frequency.