One of the defining qualities of living with HIV has been that it is incurable, and this basic fact has powerfully formed and disrupted individual, organizational, and institutional identities. But now this basic fact is contested. Today one individual appears to be cured. Several individuals are “post-treatment controllers,” having undetectable viral loads following a period of early antiretroviral therapy. HIV cure research, once unimaginable, is now at the center of public and scientific attention. Curing HIV has become a strategic priority of the International AIDS Society and the National Institute of Allergy and Infectious Diseases at the US National Institutes of Health, spurring the development of global HIV cure collaborations and advancing initial clinical research efforts. On both clinical and public health grounds, the identification of an effective HIV cure would be a great achievement. It could decrease morbidity and mortality associated with HIV infection, paving the way for comprehensive public health control efforts. At the same time, curing HIV is best conceived not simply as an absolute medical victory, but also as a social intervention whose meaning and effects are complex and uncertain.