According to a common view, in a case involving an indivisible good and several potential beneficiaries, who are equal in every relevant respect, there is a non-instrumental reason to allocate the benefit in a way that gives each an equal chance to receive the benefit. In this paper, I argue that this view is incompatible with several plausible and widely held assumptions. I emphasize especially the assumption that the distributive role of chances is secondary to that of benefits in an (...) important sense: the value of allocating chances is related to the ways in which it is possible to allocate the relevant benefits. Specifically, chances should be allocated only when it is impossible or too costly to allocate benefits in accordance with the relative importance of the reasons in favor of allocating the relevant benefit to each potential beneficiary. Given this assumption, I argue that the fact that there is no relation between the distributive concern for chances and other distributive concerns suggests that we should reject the view that chances have a distributive role that is not merely instrumental. (shrink)