The concept of reuse in process models is extensively studied in the literature. Sub-processes, process templates, process variants, and process reference models are employed as reusable elements for process modeling. Additionally, the notion of process fragments has been introduced to capture parts of a process model and store them for later reuse. In contrast, concepts for reuse of processes that cross the boundaries of organizations, i.e., choreographies, have not yet been studied in the appropriate level of detail. In this paper, we introduce the concept of choreography fragments as reusable elements for choreography modeling. Choreography fragments can be extracted from choreography models, adapted, stored, and inserted into new models. We provide a formal model for choreography fragments and identify a set of patterns constituting frequently occurring meaningful choreography fragments.