  An oscillating universe cycles through a series of expansions and
contractions. We propose a model in which ``phantom'' energy with a
supernegative pressure ($p < - \rho$) grows rapidly and dominates the late-time
expanding phase. The universe's energy density is then so large that the
effects of quantum gravity are important at both the beginning and the end of
each expansion (or contraction). The bounce can be caused by high energy
modifications to the Friedmann equation governing the expansion of the
universe, which make the cosmology nonsingular. The classic black hole
overproduction of oscillating universes is resolved due to their destruction by
the phantom energy.
