We design and build the first neural temporal dependency parser. It utilizes a neural ranking model with minimal feature engineering, and parses time expressions and events in a text into a temporal dependency tree structure. We evaluate our parser on two domains: news reports and narrative stories. In a parsing-only evaluation setup where gold time expressions and events are provided, our parser reaches 0.81 and 0.70 f-score on unlabeled and labeled parsing respectively, a result that is very competitive against alternative approaches. In an end-to-end evaluation setup where time expressions and events are automatically recognized, our parser beats two strong baselines on both data domains. Our experimental results and discussions shed light on the nature of temporal dependency structures in different domains and provide insights that we believe will be valuable to future research in this area.