This paper builds a model with imperfect competition in the banking sector. In the model, banks issue deposits and make loans, and deposits can be used as payment instruments by households. We use the model to assess the general equilibrium effects of introducing a central bank digital currency (CBDC). We identify a new channel through which the CBDC can improve the efficiency of bank intermediation and increase lending and aggregate output even if its usage is low, i.e., the CBDC serves as an outside option for households, thus limiting banks' market power in the deposit market. We then calibrate the model to the US economy and find that with a proper interest rate, CBDC can raise bank lending by around 7% and increase output by around 1%. The quantitative results are sensitive to parameters governing the acceptance of different means of payments and the degree of competition in the deposit market.