  In this paper we take into account the existence of Gribov copies in a
four-dimensional Yang-Mills theory in the Landau gauge with an effective
Lorentz symmetry breaking, induced by the Carroll-Field-Jackiw (CFJ) term. The
self consistent gap equation of the Gribov parameter is properly derived and,
provided observational bounds to the amplitude of the CFJ parameter in the
$SU(2)$ gauge theory, a qualitative analysis of the Gribov parameter and of the
poles of the propagator is developed.
