  In this paper we prove the existence of infinitely many closed Reeb orbits
for a certain class of contact manifolds. This result can be viewed as a
contact analogue of the Hamiltonian Conley conjecture. The manifolds for which
the contact Conley conjecture is established are the pre-quantization circle
bundles with aspherical base. As an application, we prove that for a surface of
genus at least two with a non-vanishing magnetic field, the twisted geodesic
flow has infinitely many periodic orbits on every low energy level.
