  We consider the pairing induced in a strictly 2D electron gas (2DEG) by a
proximate insulating film with polarizable localized excitations. Within a
model of interacting 2D electrons and localized two-level systems, we calculate
the critical temperature $T_c$ as a function of applied voltage and for
different materials properties. Assuming that a sufficient carrier density can
be induced in a field-gated device, we argue that superconductivity may be
observable in such systems. $T_c$ is found to be a nonmonotonic function of
both electric field and the excitation energy of the two-level systems.
