The range expansion of zebra mussels (Dreissena polymorpha) in North America has been rapid and costly in both economic and ecological terms. Joint social, political, and scientific ventures such as the 100th Meridian Initiative aim to reduce the spread of zebra mussels by eliminating the unintended transport of the species and preventing its westward expansion. Here we forecast the potential distribution of zebra mussels in the United States by applying a machine-learning algorithm for nonparametric prediction of species distributions (genetic algorithm for rule-set production, or GARP) to data about the current distribution of zebra mussels in the United States and 11 environmental and geological covariates. Our results suggest that much of the American West will be uninhabitable for zebra mussels. Nonetheless, some catchments along the West Coast and in the southeastern United States exhibit considerable risk of invasion and should be monitored carefully. Possible propagule dispersal to these places should be managed proactively.