COVID-19 Testing, Reaching, And Contacting Everyone Act or the TRACE Act This bill authorizes the Centers for Disease Control and Prevention (CDC) to award grants for testing, contact tracing, monitoring, and other activities to address COVID-19 (i.e., coronavirus disease 2019). Entities such as federally qualified health centers, nonprofit organizations, and certain hospitals and schools are eligible to receive such grants. In awarding the grants, the CDC shall prioritize applicants that (1) operate in hot spots and medically underserved communities, and (2) agree to hire individuals from the communities where grant activities occur.