An opportunistic scheduling scheme is proposed for the downlink of a coordinated multi-point (CoMP) system, which exploits both spatial multiplexing and multiuser diversity gains while maintaining fair resource sharing among users. The proposed scheduling scheme consists of two steps in each time slot: selecting a base station (BS) at each user, and then selecting a user at each BS. Although the proposed scheme selects users in a distributed manner, the channels among the selected users are proved to be orthogonal when the number of users approaches infinity. Simulation results demonstrate that the proposed scheme yields a better throughput than the existing scheduling schemes designed for fair resource sharing in CoMP systems.