Video-on-demand in the Internet has become an immensely popular service in recent years. But due to its high bandwidth requirements and popularity, it is also a costly service to provide. We consider the design and potential benefits of peer-assisted video-on-demand, in which participating peers assist the server in delivering VoD content. The assistance is done in such a way that it provides the same user quality experience as pure client-server distribution. We focus on the single-video approach, whereby a peer only redistributes a video that it is currently watching. Using a nine-month trace from a client-server VoD deployment for MSN Video, we assess what the 95 percentile server bandwidth costs would have been if a peer-assisted employment had been instead used. We show that peer-assistance can dramatically reduce server bandwidth costs, particularly if peers prefetch content when there is spare upload capacity in the system. We consider the impact of peer-assisted VoD on the cross-traffic among ISPs. Although this traffic is significant, if care is taken to localize the P2P traffic within the ISPs, we can eliminate the ISP cross traffic while still achieving important reductions in server bandwidth. We also develop a simple analytical model which captures many of the critical features of peer-assisted VoD, including its operational modes.