The COVID-19 outbreak is the most serious test of the international system since the 2008 global financial crisis. Rather than cooperate to contain and respond to a common threat, the world's leading powers—the United States and China—have increasingly blamed each other through wildly speculative theories about the origins of the virus. The World Health Organization sought to coordinate a global response, but it has been hamstrung and has come under attack. Given past cooperation between major powers to mobilize and eradicate smallpox and previous US leadership to fight HIV/AIDS and the 2014 West African Ebola crisis, the limited cooperation and lack of leadership are puzzling. What explains the anemic global response to date? This article draws from structural international relations theory to suggest a partial but somewhat dissatisfying answer. International organizations are inherently weak and now face opposition by major powers. The international system simultaneously incentivizes states to cooperate and address common threats, but it also encourages countries to take care of themselves, potentially at the expense of others. Which of these motives dominates cannot be explained by structural theory, thus requiring us to look to other factors such as the attributes of states and leaders themselves.