Numerous polls suggest that COVID-19 is a profoundly partisan issue in the United States. Using the geotracking data of 15 million smartphones per day, we found that US counties that voted for Donald Trump (Republican) over Hillary Clinton (Democrat) in the 2016 presidential election exhibited 14% less physical distancing between March and May 2020. Partisanship was more strongly associated with physical distancing than numerous other factors, including counties' COVID-19 cases, population density, median income, and racial and age demographics. Contrary to our predictions, the observed partisan gap strengthened over time and remained when stay-at-home orders were active. Additionally, county-level consumption of conservative media (Fox News) was related to reduced physical distancing. Finally, the observed partisan differences in distancing were associated with subsequently higher COVID-19 infection and fatality growth rates in pro-Trump counties. Taken together, these data suggest that US citizens' responses to COVID-19 are subject to a deep-and consequential-partisan divide.