Peer-to-peer (P2P) technology has been broadly adopted in live media streaming in recent years. In this paper, we consider a P2P streaming network where a server generates content chunks, and transmits each chunk to a randomly selected peer. Peers then exchange chunks among themselves according to some chunk selection policy. While the performance of different chunk selection policies has been intensively analyzed assuming no peer arrival or departure, the impact of peer churn on P2P live streaming has not been well understood yet. We show that unlike in the static network scenario, larger buffer size does not necessarily result in higher playout probability in the presence of peer churn. We further analyze the relation between the buffer size, playout probability and peer churn under different chunk selection policies and characterize the impact of peer churn on the performance of these chunk selection policies via both theoretical analysis and simulations.