We reexamine the core in the adverse selection insurance economy first studied by Rothschild and Stiglitz (1976). Defining blocking in a way that takes private information into account, the core is sometimes empty. We define the coalition-proof core as the set of allocations which are blocked only by allocations which are themselves blocked by coalition- proof allocations. This definition is closely related to Coalition Proof Nash Equilibrium, introduced by Bernheim, Peleg and Whinston (1987). We prove that the coalition-proof core consists of the Miyazaki allocation--the Pareto-optimal allocation most preferred by low-risk agents. The coalition-proof core is always nonempty in this economy and has attractive continuity properties. Cross-subsidization can occur in the coalition-proof core.