A three-dimensional nonlinear dynamo process is identified in rotating plane Couette flow in the Keplerian regime. It is analogous to the hydrodynamic self-sustaining process in nonrotating shear flows and relies on the magnetorotational instability of a toroidal magnetic field. Steady nonlinear solutions are computed numerically for a wide range of magnetic Reynolds numbers but are restricted to low Reynolds numbers. This process may be important to explain the sustenance of coherent fields and turbulent motions in Keplerian accretion disks, where all its basic ingredients are present.