How effective are restrictions on geographic mobility in limiting the spread of the COVID-19 pandemic? Using zip code data for Atlanta, Boston, Chicago, New York (NYC), and Philadelphia, we estimate that total COVID-19 cases per capita decrease on average by approximately 20 percent for every ten percentage point fall in mobility between February and May 2020. To address endogeneity concerns, we instrument for travel by the share of workers in remote work friendly occupations, and find a somewhat larger average decline of COVID-19 cases per capita of 27 percent. Using weekly data by zip code for NYC and a panel data specification including week and zip code fixed effects, we estimate a similar average decline of around 17 percent, which becomes larger when we measure mobility using NYC turnstile data rather than cellphone data. We find substantial heterogeneity across both space and over time, with stronger effects for NYC, Boston and Philadelphia than for Atlanta and Chicago, and the largest estimated coefficients for NYC in the early stages of the pandemic.