Language models are increasingly attracting interest from writers. However, such models lack long-range semantic coherence, limiting their usefulness for longform creative writing. We address this limitation by applying language models hierarchically, in a system we call Dramatron. By building structural context via prompt chaining, Dramatron can generate coherent scripts and screenplays complete with title, characters, story beats, location descriptions, and dialogue. We illustrate Dramatron's usefulness as an interactive co-creative system with a user study of 15 theatre and film industry professionals. Participants co-wrote theatre scripts and screenplays with Dramatron and engaged in open-ended interviews. We report critical reflections both from our interviewees and from independent reviewers who watched stagings of the works to illustrate how both Dramatron and hierarchical text generation could be useful for human-machine co-creativity. Finally, we discuss the suitability of Dramatron for co-creativity, ethical considerations -- including plagiarism and bias -- and participatory models for the design and deployment of such tools.