  An oscillating universe cycles through a series of expansions and
contractions. We propose a model in which ``phantom'' energy with $p < -\rho$
grows rapidly and dominates the late-time expanding phase. The universe's
energy density is 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, which
make the cosmology nonsingular. The classic black hole overproduction of
oscillating universes is resolved due to their destruction by the phantom
energy.
