We propose a peer-to-peer multimedia streaming solution based on the BitTorrent content-distribution protocol. Our proposal includes two modifications that allow it to deliver multimedia data on time. First, we replace the rarest-first chunk downloading policy of BitTorrent by a policy requiring peers to download first the chunks that they will watch in the near future. Second, we introduce a new randomized tit-for-tat peer selection policy that gives free tries to a larger number of peers and lets them participate sooner in the media distribution. Our simulations indicate that both changes are required to achieve a good streaming quality.