We introduce a new dataset of conversational speech representing English from India, Nigeria, and the United States. The Multi-Dialect Dataset of Dialogues (MD3) strikes a new balance between open-ended conversational speech and task-oriented dialogue by prompting participants to perform a series of short information-sharing tasks. This facilitates quantitative cross-dialectal comparison, while avoiding the imposition of a restrictive task structure that might inhibit the expression of dialect features. Preliminary analysis of the dataset reveals significant differences in syntax and in the use of discourse markers. The dataset, which will be made publicly available with the publication of this paper, includes more than 20 hours of audio and more than 200,000 orthographically-transcribed tokens.