  We derive a gauge theoretic invariant of integral homology 3-spheres which
counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign
given by spectral flow. To compensate for the dependence of this sum on
perturbations, the invariant includes contributions from the reducible,
perturbed flat orbits. Our formula for the correction term generalizes that
given by Walker in his extension of Casson's SU(2) invariant to rational
homology 3-spheres.
