  The gauge covariant lattice Dirac operator D which has recently been proposed
by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral
symmetry. The operator also avoids a doubling of fermion species, but its
locality properties are not obvious. We now prove that D is local (with
exponentially decaying tails) if the gauge field is sufficiently smooth at the
scale of the cutoff. Further analytic and numerical studies moreover suggest
that the locality of the operator is in fact guaranteed under far more general
conditions.
