Due to its promising performance in a wide range of practical scenarios, Rate-Splitting (RS) has recently received significant attention in academia for the downlink of communication systems. In this letter, we propose and analyse a Cooperative Rate-Splitting (CRS) strategy based on the three-node relay channel where the transmitter is equipped with multiple antennas. By splitting user messages and linearly precoding common and private streams at the transmitter, and opportunistically asking the relaying user to forward its decoded common message, CRS can efficiently cope with a wide range of propagation conditions (disparity of user channel strengths and directions) and compensate for the performance degradation due to deep fading. The precoder design and the resource allocation are optimized by solving the Weighted Sum Rate (WSR) maximization problem. Numerical results demonstrate that our proposed CRS scheme can achieve an explicit rate region improvement compared to its non-cooperative counterpart and other cooperative strategies (such as cooperative NOMA).