Storytelling plays a central role in human socializing and entertainment. However, much of the research on automatic storytelling generation assumes that stories will be generated by an agent without any human interaction. In this paper, we introduce the task of collaborative storytelling, where an artificial intelligence agent and a person collaborate to create a unique story by taking turns adding to it. We present a collaborative storytelling system which works with a human storyteller to create a story by generating new utterances based on the story so far. We constructed the storytelling system by tuning a publicly-available large scale language model on a dataset of writing prompts and their accompanying fictional works. We identify generating sufficiently human-like utterances to be an important technical issue and propose a sample-and-rank approach to improve utterance quality. Quantitative evaluation shows that our approach outperforms a baseline, and we present qualitative evaluation of our system's capabilities.