Bank markups have risen substantially, dispersion across banks has increased, and large banks now charge higher markups than smaller institutions. We develop a general equilibrium model in which persistent borrower and depositor relationships endogenously generate heterogeneous bank market power. Banks are dynamic two-sided intermediaries that compete for customers while inheriting partially captive borrower and depositor bases. Relationship capital creates a trade-off between current margins and future franchise value, generating endogenous loan markups and deposit markdowns that vary across banks. Regulatory constraints and costly external equity make market power on one side of the balance sheet affect pricing on the other, linking deposit markdowns and loan markups. Quantitatively, two-sided bank market power has sizable macroeconomic implications, reducing financial intermediation and lowering aggregate output. A permanent increase in the safe rate alters franchise values, leading banks with different customer bases to adjust loan and deposit rates differently.