  The properties of the quark propagator in Landau gauge in quenched QCD are
examined for the overlap quark action. The overlap quark action satisfies the
Ginsparg-Wilson relation and as such provides an exact lattice realization of
chiral symmetry. This in turn implies that the quark action is free of ${\cal
O}(a)$ errors. We present results using the standard Wilson fermion kernel in
the overlap formalism on a $12^3\times 24$ lattice at a spacing of 0.125 fm. We
obtain the nonperturbative momentum-dependent wavefunction renormalization
function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of
bare masses. We perform a simple extrapolation to the chiral limit for these
functions. We clearly observe the dynamically generated infrared mass and
confirm the qualitative behavior found for the Landau gauge quark propagator in
earlier studies. We attempt to extract the quark condensate from the asymptotic
behavior of the mass function in the chiral limit.
