  We investigate QCD with a large number of massless flavors with the aid of
renormalization group flow equations. We determine the critical number of
flavors separating the phases with and without chiral symmetry breaking in
SU(Nc) gauge theory with many fermion flavors. Our analysis includes all
possible fermionic interaction channels in the pointlike four-fermion limit.
Constraints from gauge invariance are resolved explicitly and regulator-scheme
dependencies are studied. Our findings confirm the existence of an Nf window
where the system is asymptotically free in the ultraviolet, but remains
massless and chirally invariant on all scales, approaching a conformal fixed
point in the infrared. Our prediction for the critical number of flavors of the
zero-temperature chiral phase transition in SU(3) is Nf^{cr}=10.0\pm
  0.29(fermion)[+1.55;-0.63](gluon), with the errors arising from
approximations in the fermionic and gluonic sectors, respectively.
