Cooperative video games, where multiple participants must coordinate by communicating and reasoning under uncertainty in complex environments, yield a rich source of language data. We collect the Portal Dialogue Corpus: a corpus of 11.5 hours of spoken human dialogue in the co-op mode of the popular Portal 2 virtual puzzle game, comprising 24.5K total utterances. We analyze player language and behavior, identifying a number of linguistic phenomena that rarely appear in most existing chitchat or task-oriented dialogue corpora, including complex spatial reference, clarification and repair, and ad-hoc convention formation. To support future analyses of language use in complex, situated, collaborative problem-solving scenarios, we publicly release the corpus, which comprises player videos, audio, transcripts, game state data, and both manual and automatic annotations of language data.