  In the continuum, a topological obstruction to the vanishing of the
non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac
operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family
of Dirac operators in 2n dimensions. In this paper an analogous result is
derived for chiral fermions on the lattice in the Overlap formulation. This
involves deriving an Index Theorem for a family of lattice Dirac operators
satisfying the Ginsparg--Wilson relation. The index density is proportional to
Luescher's topological field in 2n+2 dimensions.
