Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are much more complicated than we can imagine and relations can be high-order. In light of this, there is a need to think beyond pairwise interactions. Hypergraph provides a natural way to model complex high-order relations, and its potential for social recommendation has rarely been fully exploited. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Each channel in the network encodes a motif-induced hypergraph which depicts a common high-order user relation pattern in social recommender systems. By aggregating the embeddings learned via multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation (pooling/attention mechanism) might obscure the features of different types of high-order information and discard the inherent characteristics of users. To compensate for the aggregating loss and fully inherit the rich information in the hypergraphs, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network. The self-supervised task serves as an auxiliary task to regularize the user representation by hierarchically maximizing the mutual information between representations of the user, the user- centered sub-hypergraph, and the hypergraph in each channel, with the intuition that the aggregated user representation should reflect the user node’s local and global high-order connectivity patterns in different hypergraphs. Experimental results on multiple real-world datasets show that the proposed model outperforms the state-of-the-art baselines and further analysis verifies the rationality and effectiveness of the self-supervised task.