An electrostatic imaging mechanism is presented which allows atomic resolution of the surface of ionic crystals by atomic force microscopy (AFM). In the x-y plane the electrostatic field due to the ion charges reflects the periodicity of the surface lattice. If the tip of the AFM stylus is polarizable, an attractive force between tip and sample will exist and allow imaging of the surface in a noncontact mode. It is shown that the decay length of the electrostatic interaction in the z direction is sufficiently short for atomic resolution to be achieved not only with a hypothetical tip consisting of only one atom but also by a more realistic tip of parabolic shape with a radius of 30 nm. The theory is applied to the (001) surface of KBr.