  We examine the role of instantons in the zero-temperature chiral phase
transition in an SU(N) gauge theory. For a range of N_f (the number of fermion
flavors) depending on N, the theory exhibits an infrared fixed point at
coupling $\alpha_*$. As N_f decreases, $\alpha_*$ increases, and it eventually
exceeds a critical value sufficient to trigger chiral symmetry breaking. For
the case N = 2, we estimate the critical values of N_f and $\alpha_*$ due to
instantons by numerically solving a gap equation with an instanton-generated
kernel. We find instanton effects of strength comparable to that of gluon
exchange.
