  We search for all Poisson brackets for the BTZ black hole which are
consistent with the geometry of the commutative solution and are of lowest
order in the embedding coordinates. For arbitrary values for the angular
momentum we obtain two two-parameter families of contact structures. We obtain
the symplectic leaves, which characterize the irreducible representations of
the noncommutative theory. The requirement that they be invariant under the
action of the isometry group restricts to $R\times S^1$ symplectic leaves,
where $R$ is associated with the Schwarzschild time. Quantization may then lead
to a discrete spectrum for the time operator.
