  We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the
collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac
operator. The mechanism, originating from complex Burger's-like equation for
viscid, pressureless, one-dimensional flow of eigenvalues, is similar to
recently observed weak-strong coupling phase transition in large $N_c$
Yang-Mills theory. The spectral viscosity is proportional to the inverse of the
size of the random matrix that replaces the Dirac operator in the universal
(ergodic) regime. We obtain the exact scaling function and critical exponents
of the chiral phase transition for the averaged characteristic polynomial for
$N_c \ge3$ QCD. We reinterpret our results in terms of known properties of
chiral random matrix models and lattice data.
