Summarization of clinical narratives is a long-standing research problem. Here, we introduce the task of hospital-course summarization. Given the documentation authored throughout a patient's hospitalization, generate a paragraph that tells the story of the patient admission. We construct an English, text-to-text dataset of 109,000 hospitalizations (2M source notes) and their corresponding summary proxy: the clinician-authored Brief Hospital Course'' paragraph written as part of a discharge note. Exploratory analyses reveal that the BHC paragraphs are highly abstractive with some long extracted fragments; are concise yet comprehensive; differ in style and content organization from the source notes; exhibit minimal lexical cohesion; and represent silver-standard references. Our analysis identifies multiple implications for modeling this complex, multi-document summarization task.