We introduce Bayesian Coalitional Games (BCGs), a generalization of classical coalitional games to settings with uncertainties. We define the semantics of BCG using the partition model, and generalize the notion of payoffs to contracts among agents. To analyze these games, we extend the solution concept of the core under three natural interpretations—ex ante, ex interim, and ex post—which coincide with the classical definition of the core when there is no uncertainty. In the special case where agents are risk-neutral, we show that checking for core emptiness under all three interpretations can be simplified to linear feasibility problems similar to that of their classical counterpart.