Incentive mechanisms are essential components of peer-to-peer systems for file sharing such as BitTorrent, since they enforce peers to share their resources and to participate. Recent P2P systems that distribute live multimedia streams take their inspiration from BitTorrent, but have not defined incentive mechanisms appropriate to the nature of continuous media. In this article, we uncover the way that the incentive mechanisms in BitTorrent are not well suited to streaming live multimedia, and based on P2P systems that we have measured, we propose a new incentive mechanism designed for distribution of live multimedia streaming over a P2P network.