  In this paper, we generalize the Kobayashi pseudo-distance to complex
manifolds which admit holomorphic bracket generating distributions. The
generalization is based on Chow's theorem in sub-Riemannian geometry. Let G be
a linear semisimple Lie group. For a complex $G$-homogeneous manifold M with a
G-invariant holomorphic bracket generating distribution D, we prove that (M,D)
is Kobayashi hyperbolic if and only if the universal covering of M is a
canonical flag domain and the induced distribution is the superhorizontal
distribution.
