  We construct a Wick-type deformation quantization of contact metric
manifolds. The construction is fully canonical and involves no arbitrary
choice. Unlike the case of symplectic or Poisson manifolds, not every classical
observable on a general contact metric manifold can be promoted to a quantum
one due to possible obstructions to quantization. We prove, however, that all
these obstructions disappear for Sasakian manifolds.
