The rational behavior of a coalition requires the informational precondition that its members take into account the behavior and beliefs of others. In noncooperative games, we define Bayesian coalitional rationality as a mode of collective behavior that no coalition of players wishes to change, in the sense that there is no coalition-wise common belief that mutual gains can be achieved through tacit coalitional agreement. We establish a fundamental possibility result: the assumption of Bayesian coalitional rationality and common belief of Bayesian coalitional rationality is attainable in a finite model. Under a belief-richness condition, this assumption characterizes the solution concept of Bayesian coalitional rationalizability. Our approach also provides a novel notion of individual rationality in game situations where players may be uncertain about their own types and strategy choices.