  We study the non-perturbative production of gluon pairs from a constant SU(3)
chromo-electric background field via the Schwinger mechanism. We fix the
covariant background gauge with an arbitrary gauge parameter \alpha. We
determine the transverse momentum distribution of the gluons, as well as the
total probability of creating pairs per unit space time volume. We find that
the result is independent of the covariant gauge parameter \alpha used to
define arbitrary covariant background gauges. We find that our non-perturbative
result is both gauge invariant and gauge parameter \alpha independent.
