We present a novel multi-agent RL approach, Selective Multi-Agent Prioritized Experience Relay, in which agents share with other agents a limited number of transitions they observe during training. The intuition behind this is that even a small number of relevant experiences from other agents could help each agent learn. Unlike many other multi-agent RL algorithms, this approach allows for largely decentralized training, requiring only a limited communication channel between agents. We show that our approach outperforms baseline no-sharing decentralized training and state-of-the art multi-agent RL algorithms. Further, sharing only a small number of highly relevant experiences outperforms sharing all experiences between agents, and the performance uplift from selective experience sharing is robust across a range of hyperparameters and DQN variants.