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We introduce the task ofstory fragment stitching,which is the process of automatically aligning andmerging event sequences of partial tellings of astory (i.e.,story fragments). We assume that eachfragment contains at least one event from the storyof interest, and that every fragment shares at leastone event with another fragment. We propose agraph-based unsupervised approach to solving thisproblem in which events mentions are representedas nodes in the graph, and the graph is compressedusing a variant of model merging to combine nodes.The goal is for each node in the final graph to con-tain only coreferent event mentions. To find coref-erent events, we use BERT contextualized embed-ding in conjunction with atf-idfvector representa-tion. Constraints on the merge compression pre-serve the overall timeline of the story, and the finalgraph represents the full story timeline. We evalu-ate our approach using a new annotated corpus ofthe partial tellings of the story of Moses found inthe Quran, which we release for public use. Ourapproach achieves a performance of 0.63F1score