  We conjecture that, in certain cases, quantum dynamics is consistent in the
presence of closed timelike curves. We consider time dependent orbifolds of
three dimensional Minkowski space describing, in the limit of large AdS radius,
BTZ black holes inside the horizon. Although perturbative unitarity fails, we
show that, for discrete values of the gravitational coupling, particle
propagation is consistent with unitarity. This quantization corresponds to the
quantization of the black hole angular momentum, as expected from the dual CFT
description. Note, however, that we recover this result by analyzing the
physics inside the horizon and near the singularity. The spacetime under
consideration has no AdS boundary, and we are therefore not using any
assumption regarding a possible dual formulation. We perform the computation at
very low energies, where string effects are irrelevant and interactions are
dominated by graviton exchange in the eikonal regime. We probe the non-causal
structure of space-time to leading order, but work to all orders in the
gravitational coupling.
