Anaphora resolution is a traditional task in the natural language processing community, defined as a cohesion phenomenon where one entity points back to a previous entity. Event discourse deixis (EDD) is a kind of more complex anaphora in which the anaphors refer to event descriptions such as sentences or clauses. Event discourse deixis resolution (EDDR) is able to help machines understand the richer linguistic and semantic information in the discourse. However, compared to anaphora resolution, EDDR has received relatively less research attention. In this work, we investigate the EDDR task by designing the corresponding dataset and model. First, we manually construct a high-quality Chinese corpus for EDDR, including 4,417 documents and 5,929 event chains that consist of event antecedents and anaphors. Second, we propose a deep neural network model for EDDR, which formulates the task into two subtasks, namely event anaphor recognition and event antecedent recognition. Our model is trained under the two subtasks jointly so that the EDDR task can be performed end-to-end. Besides our final model, we also build 7 pipeline and joint models as baselines to build comprehensive benchmarks for follow-up research. Experimental results on our EDDR dataset show that our model outperforms all the baselines and achieves about 53%, 44%, 53% and 63% F1s using standard anaphora resolution metrics such as CoNLL, MUC, B3 and Ceafe. The performances show that EDDR is a challenging task and worth researching in the future. Our dataset and model will be released to facilitate the follow-up research.