  The ground state of a spin 1/2 nearest neighbor quantum Heisenberg
antiferromagnet on the pyrochlore lattice is investigated using a large $N$
SU(N) fermionic mean field theory. We find several mean field states, of which
the state of lowest energy upon Gutzwiller projection, is a parity and time
reversal breaking chiral phase with a unit monopole flux exiting each
tetrahedron. This "monopole flux" state has a Fermi surface consisting of 4
lines intersecting at a point. At mean field the low-energy excitations about
the Fermi surface are gapless spinons. An analysis using the projective
symmetry group of this state suggests that the state is stable to small
fluctuations which neither induce a gap, nor alter the unusual Fermi surface.
