This paper studies the incentives of a merchant to bypass a payment platform by issuing private cards. In our model, a payment platform allocates the total cost of a card transaction between a monopolistic issuer and a monopolistic acquirer by choosing an "interchange fee". We determine how the level of the interchange fee impacts a merchant's decision to issue private cards, if there are strategic interactions between merchants. We prove that the payment platform can only deter entry by lowering the level of the interchange fee. If the payment platform chooses to accommodate entry, we find that the total user surplus increases, but that entry is beneficial to social welfare only if the entry cost is sufficiently low.