APPARENT velocities greater than the speed of light (superluminal motion) have been inferred for radio-emitting components in a number of distant quasars and active galactic nuclei1. These components move away from the central sources (generally thought to be super-massive black holes) at rates that seem to imply velocities greater than c. The accepted explanation is that clouds of plasma are ejected in opposite directions from the central source at speeds close to (but less than) that of light, and that relativistic effects lead to the apparent superluminal motion2. But the extreme distance of the objects observed so far introduces many uncertainties into this interpretation3. Here we present observations of the first apparent superluminal motion ever detected in a source within our own Galaxy. The optical, infrared and X-ray properties4,5 of the counterpart suggest that the source is either a neutron star or a black hole that is ejecting matter in a process similar to, but on a smaller scale than that seen in quasars. Because of its relative proximity, this superluminal microquasar may offer the best opportunity to gain a general understanding of relativistic ejections seen elsewhere in the Universe.