We introduce the task of story fragment stitching, which is the process of automatically aligning and merging event sequences of partial tellings of a story (i.e., story fragments). We assume that each fragment contains at least one event from the story of interest, and that every fragment shares at least one event with another fragment. We propose a graph-based unsupervised approach to solving this problem in which events mentions are represented as nodes in the graph, and the graph is compressed using a variant of model merging to combine nodes. The goal is for each node in the final graph to contain only coreferent event mentions. To find coreferent events, we use BERT contextualized embedding in conjunction with a tf-idf vector representation. Constraints on the merge compression preserve the overall timeline of the story, and the final graph represents the full story timeline. We evaluate our approach using a new annotated corpus of the partial tellings of the story of Moses found in the Quran, which we release for public use. Our approach achieves a performance of 0.63 F1 score.