The idea that clades might be units of selection, defended by a number of biologists and philosophers of biology, is critically examined. I argue that only entities which reproduce, i.e. leave offspring, can be units of selection, and that a necessary condition of reproduction is that the offspring entity be able, in principle, to outlive its parental entity. Given that clades are monophlyetic by definition, it follows that clades do not reproduce, so it makes no sense to talk about a clade's fitness, so clade selection is impossible. Three possible responses to this argument are examined and found wanting.