  Calculations of the chiral condensate $\langle \bar{\psi} \psi \rangle$ on
the lattice using staggered fermions and the Lanczos algorithm are presented.
Three gauge fields are considered: the quenched non-Abelian field, the Abelian
field projected in the maximal Abelian gauge, and the monopole field further
decomposed from the Abelian field. The results show that the Abelian monopoles
largely reproduce the chiral condensate values of the full non-Abelian theory,
both in SU(2) and in SU(3).
