How should administrative law cope with genuine uncertainty, in which probabilities cannot be attached to outcomes? I argue that there is an important category of agency decisions under uncertainty is which it is rational to be arbitrary. Rational arbitrariness arises when no first-order reason can be given for the agency’s choice one way or another within a certain domain, yet the agency has valid second-order reasons to make some choice or other. When these conditions obtain, even coin-flipping may be a perfectly rational strategy of decisionmaking for agencies. Courts should defer to rationally arbitrary decisions by agencies. There is a proper role for courts in ensuring that agencies have adequately invested resources in information-gathering, which may dispel uncertainty. Yet in some cases the value of further investments in information-gathering will itself be genuinely uncertain. If so, courts should defer to agencies’ second-order choices about informational investments on the same grounds that justify deference to agencies’ first-order choices under uncertainty.