Quit Because of COVID-19 Act This bill provides for Medicaid and Children's Health Insurance Program (CHIP) coverage of certain tobacco cessation services during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019), as well as for two years after the emergency period ends. Specifically, the bill provides for coverage 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. The bill excludes such items and services from cost-sharing and applies an enhanced Federal Medical Assistance Percentage (i.e., federal matching rate).