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To understand a narrative, it is essential to comprehend the temporal event flows, especially those associated with main characters; however, this can be challenging with lengthy and unstructured narrative texts. To address this, we introduce NECE, an open-access, document-level toolkit that automatically extracts and aligns narrative events in the temporal order of their occurrence. Through extensive evaluations, we show the high quality of the NECE toolkit and demonstrates its downstream application in analyzing narrative bias regarding gender. We also openly discuss the shortcomings of the current approach, and potential of leveraging generative models in future works. Lastly the NECE toolkit includes both a Python library and a user-friendly web interface, which offer equal access to professionals and layman audience alike, to visualize event chain, obtain narrative flows, or study narrative bias.