  We show that it is possible for fermion condensation of the
Nambu-Jona-Lasinio type to induce a non-singular bounce that smoothly connects
a phase of slow contraction to a phase of expansion. A chiral condensate -- a
non-zero vacuum expectation value of the spinor bilinear $\langle
\bar{\Psi}\Psi \rangle$ -- can form spontaneously after a slow contraction
phase smooths and flattens the universe and the Ricci-curvature exceeds a
critical value. In this approach, a high density of spin-aligned free fermions
is not required, which avoids the problem of generating a large anisotropy and
initiating chaotic mixmaster behavior during the bounce phase.
