Trust management is a critical component in P2P file sharing systems due to the free riding and security problem. In this paper, we propose a lightweight reputation management system, R-Chain, where each peer maintains its own transaction history as the reputation. In R-Chain, each transaction is supervised by a few randomly chosen witnesses and each peer keeps a record for every transaction it has participated in. To ensure the integrity, transaction records are signed by the witnesses and organized as a chronicle chain. With very limited data stored on the network, no peer can modify or discard these transaction records without being detected. Compared with other reputation systems, our design is more lightweighted in terms of reputation maintenance and retrieval. It is scalable since each transaction only involves a constant number of peers. By recording the raw transaction history, R-Chain can also be integrated with different trust models to prevent various attacks.