ACCORDING to the reptation model of polymer diffusion(1), a polymer chain exhibits snake-like motion through the entangled mesh of surrounding molecules, in which the undulations of the chain are restricted to a tubelike region(2). The reptation model can account for many of the dynamic properties of entangled polymer solutions and melts, and has received support from observations of block copolymer diffusion across an interface(3); but reptative motion has not previously been imaged directly(4,5). Here we report such a direct observation of reptation, obtained by video microscopy of fluorescently labelled single, semiflexible filaments of actin in a solution of unlabelled actin filaments. From the restricted thermal undulations of these filaments we can measure the diameter of the confining tube, and we also observe the characteristic thermally excited sliding of the filament out of the end of the tube. We find that the chain self-diffusion coefficient decreases approximately linearly as the filament length increases, in agreement with the reptation model.