This paper develops a micro-founded general equilibrium model of payments to study the impact of a central bank digital currency (CBDC) on intermediation of private banks. If banks have market power in the deposit market, a CBDC can enhance competition, raising the deposit rate, expanding intermediation, and increasing output. A calibration to the US economy suggests that a CBDC can raise bank lending by 1.57% and output by 0.19%. These crowding-in effects remain robust, albeit with smaller magnitudes, after taking into account endogenous bank entry. We also assess the role of a non-interest-bearing CBDC as the use of cash declines.