People from all over the world use social media to share thoughts and opinions about events, and understanding what people say through these channels has been of increasing interest to researchers, journalists, and marketers alike. However, while automatically generated summaries enable people to consume large amounts of data efficiently, they do not provide the context needed for a viewer to fully understand an event. Narrative structure can provide templates for the order and manner in which this data is presented to create stories that are oriented around narrative elements rather than summaries made up of facts. In this paper, we use narrative theory as a framework for identifying the links between social media content. To do this, we designed crowdsourcing tasks to generate summaries of events based on commonly used narrative templates. In a controlled study, for certain types of events, people were more emotionally engaged with stories created with narrative structure and were also more likely to recommend them to others compared to summaries created without narrative structure.