A flash of light evokes neural activity in the brain with a delay of 30-100 milliseconds, much of which is due to the slow process of visual transduction in photoreceptors. A moving object can cover a considerable distance in this time, and should therefore be seen noticeably behind its actual location. As this conflicts with everyday experience, it has been suggested that the visual cortex uses the delayed visual data from the eye to extrapolate the trajectory of a moving object, so that it is perceived at its actual location. Here we report that such anticipation of moving stimuli begins in the retina. A moving bar elicits a moving wave of spiking activity in the population of retinal ganglion cells. Rather than lagging behind the visual image, the population activity travels near the leading edge of the moving bar. This response is observed over a wide range of speeds and apparently compensates for the visual response latency. We show how this anticipation follows from known mechanisms of retinal processing.