A Monte Carlo algorithm has been used to study the Z3 gauge glass mode
l on simple cubic lattices. The glass transition temperature, T(g), fo
r this model is 0.760 +/- 0.010J. There is an anomaly in the temperatu
re derivative of the specific heat at T(g). The freezing transition ap
pears to be describable by a picture in which localized ''nuggets'' or
ganize themselves into a state of long-range order, leading to an exte
nded state of the inverse susceptibility matrix with eigenvalue zero.
The spatial decay of the spin-glass-type gauge-invariant correlation f
unction at T(g) seems to be a power law, whose exponent, eta, is estim
ated to be 0.5 +/- 0.2.