This paper examines the response of the U.S. labor market to a large and persistent job separation rate shock, motivated by the ongoing economic effects of the COVID-19 pandemic. We use nonlinear methods to analytically and numerically characterize the responses of vacancy creation and unemployment. Vacancies decline in response to the shock when firms expect persistent job destruction and the number of unemployed searching for work is low. Quantitatively, under our baseline forecast the unemployment rate peaks at 19.7%, 2 months after the shock, and takes 1 year to return to 5%. Relative to a scenario without the shock, unemployment uncertainty rises by a factor of 11. Nonlinear methods are crucial. In the linear economy, the unemployment rate "only" rises to 9.2%, vacancies increase, and uncertainty is unaffected. In both cases, the severity of the COVID-19 shock depends on the separation rate persistence.