We attempt to determine the binding energy and the wave function of the ground state of an electron that is attracted to the surface of an ionic crystal by its image potential and is repelled from the interior of the solid. For ionic crystals, such as LiF, the electrostatic theory is inadequate and the solid must be treated as a dynamical system. For shallow levels, the correction to the electrostatic approximation is small and behaves asymptotically as z-3, where z is the distance from the surface. The mass of a shallow electron is not enhanced. For deep levels the ground-state energy is calculated by a variational procedure in the limits of both weak and strong electron-phonon coupling. For the ground-state energy of an electron trapped on the LiF surface we find the value -0.29 eV. The mass of the deeply bound electron is enhanced.