When viewed from a rotating frame the ionization of a hydrogen atom in a circularly polarized microwave field is largely governed by Coriolis forces. Although simulations show that the ionization mechanism is chaotic, we find that ionization is governed by a linear resonance. Because the electron is fed into the resonance by chaotic scattering from the core the overall ionization process, when it occurs, is chaotic. Suppression of ionization by an applied magnetic field is shown to be possible: it is due to detuning of the linear resonance by the field. [S1050-2947(98)05112-9].