Unstructured, chunk-based P2P streaming (TV and Video) systems are becoming popular and are subject of intense research. Chunk and peer selection strategies (or scheduling) are among the main driver of performance. This work presents the formal proof that there exist a distributed scheduling strategy which is able to distribute every chunk to all N peers in exactly sup(log_2(N))+1 steps. Since this is the minimum number of steps needed to distribute a chunk, the proposed strategy is optimal. Such a strategy is implementable and an entire class of deadline-based schedulers realize it. We show that at least one of the deadline-based schedulers is resilient to the reduction of the neighborhood size down to values as small as log_2(N). Selected simulation results highlighting the properties of the algorithms in realistic scenarios complete the paper.