The largest economic cost of the COVID-19 pandemic could arise from changes in behavior long after the immediate health crisis is resolved. A potential source of such a long-lived change is scarring of beliefs, a persistent change in the perceived probability of an extreme, negative shock in the future. We show how to quantify the extent of such belief changes and determine their impact on future economic outcomes. We find that the long-run costs for the U.S. economy from this channel is many times higher than the estimates of the short-run losses in output. This suggests that, even if a vaccine cures everyone in a year, the Covid-19 crisis will leave its mark on the US economy for many years to come.