  We present a new mechanism, which does not require any flavor symmetry, to
explain the small Yukawa couplings and CKM mixing angles. The Yukawa matrices
are assumed to be random at short distances and the hierarchical structure is
generated in the infrared by renormalization group flow. The generic
qualitative predictions of this mechanism are in good agreement with
observation. We give several simple examples in supersymmetric theories. We
show that our mechanism can also ameliorate the supersymmetric flavor problem,
and make predictions for the superpartner mass spectrum. The mechanism is fully
consistent with grand unification, and in SU(5)-based models of neutrino mass,
predicts a large mixing angle for muon neutrino to tau neutrino oscillations.
