The classical doctrine of the Lender of Last Resort, elaborated by Thornton (1802) and Bagehot (1873), asserts that the Central Bank should lend to "illiquid but solvent" banks under certain conditions. Several authors have argued that this view is now obsolete: when interbank markets are efficient, a solvent bank cannot be illiquid. This paper provides a possible theoretical foundation for rescuing Bagehot's view. Our theory does not rely on the multiplicity of equilibria that arises in classical models of bank runs. We build a model of banks' liquidity crises that possesses a unique Bayesian equilibrium. In this equilibrium, there is a positive probability that a solvent bank cannot find liquidity assistance in the market. We derive policy implications about banking regulation (solvency and liquidity ratios) and interventions of the Lender of Last Resort as well as on the disclosure policy of the Central Bank.