Coronavirus disease 2019 can lead to respiratory failure. Some patients require extracorporeal membrane oxygenation support. During the current pandemic, health care resources in some cities have been overwhelmed, and doctors have faced complex decisions about resource allocation. We present a case in which a pediatric hospital caring for both children and adults seeks to establish guidelines for the use of extracorporeal membrane oxygenation if there are not enough resources to treat every patient. Experts in critical care, end-of-life care, bioethics, and health policy discuss if age should guide rationing decisions.