Can informing people of high rates of community support for social distancing encourage them to do more of it? Our Mozambican study population underestimated the rate of community support for social distancing, believing support to be only 69%, while the true share was 98%. In theory, informing people of high rates of community support has ambiguous effects on social distancing, depending on whether a perceived-infectiousness effect dominates a free-riding effect. We randomly assigned a "social norm correction" treatment, informing people of true high rates of community support for social distancing. We examine an improved measure of social distancing combining detailed self-reports with reports on the respondent by others in the community. The treatment increases social distancing where COVID-19 case loads are high (where the perceived-infectiousness effect dominates), but decreases it where case loads are low (where free-riding dominates). Separately, randomized local-leader endorsements of social distancing are ineffective. As COVID-19 case loads continue to rise, interventions such as the social norm correction treatment should show increased effectiveness at promoting social distancing.