We build a model of bank concentration. Banks and entrepreneurs meet in a credit market characterized by search frictions and negotiate repayment rates `a la Nash. Banks are large in the sense that they allocate credit to more than one entrepreneur and there is bank heterogeneity in terms of their cost structure. Banks have incentives to overlend, generating scale inefficiency and overconcentration of banks. We find that overconcentration by banks generates too much concentration on the goods market too, lowering aggregate output and welfare. We use available estimates on X-efficiency and scale efficiency to calibrate the model and assess the quantitative importance of this effect: aggregate output would increase by 6.6% had the scale inefficiency been absent, while loan rates would decrease by 3.3%.