  The chirally symmetric overlap quark propagator is explored in Coulomb gauge
for the first time. This gauge is especially well suited for studying the
interrelation between confinement and chiral symmetry breaking, since
confinement can be attributed to the infrared divergence of the vector dressing
function of the inverse quark propagator. Using quenched gauge field
configurations on a $20^4$ lattice, the dressing functions of the quark
propagator as well as the dynamical quark mass function are evaluated, also in
the chiral limit. Chiral symmetry is artificially restored by removing the low
mode contribution from the quark propagator. After removing enough low-lying
modes, the dynamical quark mass function approaches the current quark mass in
the whole momentum region and goes to zero in the chiral limit. However, the
vector dressing function is unaffected by the low-mode removal. It follows that
the quark energy dispersion is still infrared divergent and quarks in such a
chiral symmetry restored phase are still confined within a hadron.
