  We investigate charged black holes coupled to a massive dilaton. It is shown
that black holes which are large compared to the Compton wavelength of the
dilaton resemble the Reissner-Nordstr\"om solution, while those which are
smaller than this scale resemble the massless dilaton solutions. Black holes of
order the Compton wavelength of the dilaton can have wormholes outside the
event horizon in the string metric. Unlike all previous black hole solutions,
nearly extremal and extremal black holes (of any size) repel each other. We
argue that extremal black holes are quantum mechanically unstable to decay into
several widely separated black holes. We present analytic arguments and
extensive numerical results to support these conclusions.
