  In the dilute instanton gas model of the QCD vacuum, one expects a strong
spatial correlation between chirality and the maxima of the Dirac eigenvectors
with small eigenvalues. Following Horvath, {\it et al.} we examine this
question using lattice gauge theory within the quenched approximation. We
extend the work of those authors by using weaker coupling, $\beta=6.0$, larger
lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In
contrast with this earlier work, we find a striking correlation between the
magnitude of the chirality density, $|\psi^\dagger(x)\gamma^5\psi(x)|$, and the
normal density, $\psi^\dagger(x)\psi(x)$, for the low-lying Dirac eigenvectors.
