We consider a multipair two-way relay network where multiple communication pairs simultaneously exchange information with the help of multiple relay nodes. All nodes are equipped with a single antenna and channel state information is available at the relay nodes. Each relay uses very simple signal processing in a distributed manner, called distributed amplify-and-forward (AF) relaying. A closed-form expression for the achievable rate is derived. We show that the distributed AF scheme outperforms conventional orthogonal relaying. When the number of relays is large, the distributed AF relaying scheme can achieve the capacity scaling given by the cut-set upper bound. Furthermore, when the number of relays grows large, the transmit powers of each terminal and of the relay can be made inversely proportional to the number of relays while maintaining a given quality-of-service. If the transmit power of each terminal is kept fixed, the transmit power of each relay can be scaled down inversely proportional to the square of the number of relays.