Some authors have called for increased research on various forms of geoengineering as a means to address global climate change. This paper focuses on the question of whether a particular form of geoengineering, namely deploying sulfate aerosols in the stratosphere to counteract some of the effects of increased greenhouse gas concentrations, would be a just response to climate change. In particular, we examine problems sulfate aerosol geoengineering (SAG) faces in meeting the requirements of distributive, intergenerational, and procedural justice. We argue that SAG faces obstacles to meeting the requirements of all three considered kinds of justice, because its impacts can harm some persons and communities much more than others; it poses serious risks to future generations; and SAG is especially prone to unilateral implementation. While we do not claim that SAG ought not to be implemented, we argue that it is the responsibility of proponents of SAG to recognize and address these ethical obstacles before advocating its implementation.