  This is the first Monte Carlo study of the hard-sphere lattice gas with
nearest neighbour exclusion on the body-centred cubic lattice. We estimate the
critical activity to be $0.7223 \pm 0.0003$. This result confirms that there is
a re-entrant phase transition of an antiferromagnetic Ising model in an
external field and a Blume-Emery-Griffiths model on the body-centred cubic
lattice.
