Global climate change, one of the most formidable sustainability problems facing humanity, is a particularly challenging collective action problem, because it is global, requiring the cooperation of all or most countries. Efforts to foster global cooperation on mitigating climate change have centered on large international agreements, with limited success. As a consequence, some have suggested that the problem could be better solved through a “building blocks” approach, where smaller numbers of states form multiple cooperative agreements, called “climate clubs”. Recently, sustainability scientists have applied a Cultural Multilevel Selection (CMLS) Framework to a variety of sustainability problems. The CMLS Framework suggests that sustainability problems requiring collective action can often be solved through competition at a higher level of organization. For example, collective action problems arising within a fishing village could be solved through competition between villages. Here, I apply the CMLS Framework to global climate change. I show that, while higher level selection may solve smaller scale sustainability problems, it cannot solve truly global problems like climate change. I also show that multilevel selection based on climate clubs is unlikely to foster cooperation in the way that some existing models suggest. I also suggest that a potential solution to climate change may be eliminating the collective action problem altogether through investment in technological innovation that might make fossil fuels costlier than their alternatives.