Peer to peer file sharing is 'booming', but meanwhile censorship of these networks and prosecution of users that share censored content are growing just as quickly. In this paper, we propose a novel notion of deniability as an easy and efficient method for users to avoid censorship and prosecution. The fundamental concept is that a given data element, which contains controversial or censored content, is also associated with neutral-content material. Hence, even a powerful adversary capable of monitoring all communication in the network and viewing the internal state of participating hosts is unable to prove a link between censored content and a user. The communication overhead required to retrieve a document is only four times greater than what is needed in a standard network. The storage required for a document is only twice as large as the document itself. Deniability is an elegant alternative to user anonymity in P2P file sharing networks. Systems that provide anonymity for users typically require greater overhead and do not guarantee anonymity against powerful, real-world adversaries.