  We give formulae for the Chen-Ruan orbifold cohomology for the orbifolds
given by a Bianchi group acting on complex hyperbolic 3-space. The Bianchi
groups are the arithmetic groups PSL\_2(A), where A is the ring of integers in
an imaginary quadratic number field. The underlying real orbifolds which help
us in our study, given by the action of a Bianchi group on real hyperbolic
3-space (which is a model for its classifying space for proper actions), have
applications in physics.We then prove that, for any such orbifold, its
Chen-Ruan orbifold cohomology ring is isomorphic to the usual cohomology ring
of any crepant resolution of its coarse moduli space.By vanishing of the
quantum corrections, we show that this result fits in with Ruan's Cohomological
Crepant Resolution Conjecture.
