There is much discussion of adopting COVID-19 immunity certificates to allow those proven to have antibodies to the SARS-CoV-2 virus that causes COVID-19 to resume normal life and help restart the economy. This article points out issues that must be considered before adopting any such program. These issues fall into six categories: the uncertain science of COVID-19 immunity; the questionable quality of COVID-19 antibody tests; practical problems with issuing such certificates; deciding how the certificates might be used; ethical and social issues they would raise, especially fairness and self-infection; and potential legal barriers. It does not ultimately take a position on whether some narrow COVID-19 immunity plans should be adopted, concluding that the answer depends on too many currently unknown conditions. But its seventh part makes recommendations to decision-makers who might consider implementing such programs.