  A model for the QCD vacuum based on a domainlike structured background gluon
field with definite duality attributed to the domains has been shown elsewhere
to give confinement of static quarks, a reasonable value for the topological
susceptibility and indications that chiral symmetry is spontaneously broken. In
this paper we study in detail the eigenvalue problem for the Dirac operator in
such a gluon mean field. A study of the local chirality parameter shows that
the lowest nonzero eigenmodes possess a definite mean chirality correlated with
the duality of a given domain. A probability distribution of the local
chirality qualitatively reproduces histograms seen in lattice simulations.
