  We construct a local, gauge-fixed, lattice Yang-Mills theory with an exact
BRST invariance, and with the same perturbative expansion as the standard
Yang-Mills theory. The ghost sector, and some of its BRST transformation rules,
are modified to get around Neuberger's theorem. A special term is introduced in
the action to regularize the Gribov horizons, and the limit where the regulator
is removed is discussed. We conclude with a few comments on what might be the
physical significance of this theory. We speculate that there may exist new
strong-interaction phases apart from the anticipated confinement phase.
