The cross section for Compton scattering can be appreciably enhanced if energy is conserved in the initial to intermediate state transition. This resonance condition cannot be satisfied for a free particle, but it can be met if the particle is in a static electric or magnetic field. In this paper an analysis is presented for light scattering from relativistic particles in an electrostatic potential. Planar channeled positrons are used as the example. It is possible to achieve a large frequency upshift from the incident to the scattered radiation, with a cross section that is many orders of magnitude larger than the usual Compton cross section.