What exactly is a “wicked problem”? It is a social or economic problem that is so complex and so interconnected with other issues that it is extraordinarily difficult or impossible to resolve. This is because all proposed resolutions generate equally complex, equally wicked problems. In this essay, I argue that precision medicine, especially in the context of the U.S. healthcare system, generates numerous wicked problems related to distributive justice. Further, I argue that there are no easy solutions to these wicked problems. The need for trade-offs is inescapable. Rough justice is the best outcome we can hope for, and that outcome requires a commitment to processes of public reason that are fair and inclusive.