The world is in the midst of a pandemic. We still know little about the disease COVID-19 or about the virus (SARS-CoV-2) that causes it. We do not have a vaccine or a treatment (aside from managing symptoms). We do not know if recovery from COVID-19 produces immunity, and if so for how long, hence we do not know if "herd immunity" will eventually reduce the risk or if a successful vaccine can be developed - and this knowledge may be a long time coming. In the meantime, the COVID-19 pandemic is presenting enormous challenges to medical research, and to clinical trials in particular. This paper identifies some of those challenges and suggests ways in which machine learning can help in response to those challenges. We identify three areas of challenge: ongoing clinical trials for non-COVID-19 drugs; clinical trials for repurposing drugs to treat COVID-19, and clinical trials for new drugs to treat COVID-19. Within each of these areas, we identify aspects for which we believe machine learning can provide invaluable assistance.