Quit Because of COVID-19 Act This bill provides for Medicaid and Children's Health Insurance Program (CHIP) coverage of certain tobacco cessation services. Specifically, the bill provides for coverage, without cost-sharing, of diagnostic, therapy, and counseling services and pharmacotherapy, including prescription and nonprescription tobacco cessation agents, that are provided under medical supervision and in accordance with specified guidelines. It also applies a 100% Federal Medical Assistance Percentage (i.e., federal matching rate) for such items and services during the public health emergency relating to COVID-19 and for two years after the emergency period ends.