We investigate the zero temperature chiral phase transition in an SU(N
) gauge theory as the number of fermions N-f is varied. We argue that
there exists a critical number of fermions N-f(c), above which there i
s no chiral symmetry breaking or confinement, and below which both chi
ral symmetry breaking and confinement set in. We estimate N-f(c) and d
iscuss the nature of the phase transition.