  We study spontaneous chiral-symmetry breaking in SU(3) QCD in terms of the
dual superconductor picture for quark confinement in the maximally Abelian (MA)
gauge, using lattice QCD Monte Carlo simulations with four different lattices
of $16^4$, $24^4$, $24^3\times 6$ at $\beta=6.0$ (i.e., the spacing $a \simeq$
0.1 fm), and $32^4$ at $\beta=6.2$ (i.e., $a \simeq$ 0.075 fm), at the quenched
level. First, in the confinement phase, we find Abelian dominance and monopole
dominance in the MA gauge for the chiral condensate in the chiral limit,using
the two different methods of i) the Banks-Casher relation with the Dirac
eigenvalue density and ii) finite quark-mass calculations with the quark
propagator and its chiral extrapolation. In the high-temperature deconfined
phase, the chiral restoration is observed also for the Abelian and the monopole
sectors. Second, we investigate local correlation between the chiral condensate
and monopoles, which topologically appear in the MA gauge. We find that the
chiral condensate locally takes a quite large value near monopoles. As an
interesting possibility, the strong magnetic field around monopoles is
responsible to chiral symmetry breaking in QCD, similarly to the magnetic
catalysis.
