  The 2D half-filled Kondo lattice model with exchange J and nearest neighbor
hopping t is considered. It is shown that this model belongs to a class of
Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may
be efficiently applied. We compute the staggered moment, spin and quasiparticle
gaps on lattice sizes up to 12 X 12. The competition between the RKKY
interaction and Kondo effect leads to a continuous quantum phase transition
between antiferromagnetic and spin-gaped insulators. This transition occurs at
J/t = 1.45 \pm 0.05.
