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The key of sequential recommendation lies in the accurate item correlation modeling. Previous models infer such information based on item co-occurrences, which may fail to capture the real causal relations, and impact the recommendation performance and explainability. In this paper, we equip sequential recommendation with a novel causal discovery module to capture causalities among user behaviors. Our general idea is firstly assuming a causal graph underlying item correlations, and then we learn the causal graph jointly with the sequential recommender model by fitting the real user behavior data. More specifically, in order to satisfy the causality requirement, the causal graph is regularized by a differentiable directed acyclic constraint. Considering that the number of items in recommender systems can be very large, we represent different items with a unified set of latent clusters, and the causal graph is defined on the cluster level, which enhances the model scalability and robustness. In addition, we provide theoretical analysis on the identifiability of the learned causal graph. To the best of our knowledge, this paper makes a first step towards combining sequential recommendation with causal discovery. For evaluating the recommendation performance, we implement our framework with different neural sequential architectures, and compare them with many state-of-the-art methods based on real-world datasets. Empirical studies manifest that our model can on average improve the performance by about 7% and 11% on f1 and NDCG, respectively. To evaluate the model explainability, we build a new dataset with human labeled explanations for both quantitative and qualitative analysis.