Banks offering credit to borrowers are faced with uncertainty about their creditworthiness. If banks obtain information about borrowers after lending to them, they are able to reject riskier borrowers when refinancing. Potential entrant banks will face an adverse-selection problem stemming from their inability to distinguish new borrowers from old borrowers who have been rejected by their previous bank. We analyze the effects of asymmetric information on the market structure of the banking industry. We characterize the equilibrium under Bertrand competition with two banks, and show than an equilibrium where a third bank enters does not exist (blockaded entry).