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Collaborative Filtering (CF) has emerged as fundamental paradigms for parameterizing users and items into latent representation space, with their correlative patterns from interaction data. Among various CF techniques, the development of GNN-based recommender systems, e.g., PinSage and LightGCN, has offered the state-of-the-art performance. However, two key challenges have not been well explored in existing solutions: i) The over-smoothing effect with deeper graph-based CF architecture, may cause the indistinguishable user representations and degradation of recommendation results. ii) The supervision signals (i.e., user-item interactions) are usually scarce and skewed distributed in reality, which limits the representation power of CF paradigms. To tackle these challenges, we propose a new self-supervised recommendation framework Hypergraph Contrastive Collaborative Filtering (HCCF) to jointly capture local and global collaborative relations with a hypergraph-enhanced cross-view contrastive learning architecture. In particular, the designed hypergraph structure learning enhances the discrimination ability of GNN-based CF paradigm, so as to comprehensively capture the complex high-order dependencies among users. Additionally, our HCCF model effectively integrates the hypergraph structure encoding with self-supervised learning to reinforce the representation quality of recommender systems, based on the hypergraph-enhanced self-discrimination. Extensive experiments on three benchmark datasets demonstrate the superiority of our model over various state-of-the-art recommendation methods, and the robustness against sparse user interaction data. Our model implementation codes are available at https://github.com/akaxlh/HCCF.