  We study the shock waves in relativistic chiral matter. We argue that the
conventional Rankine-Hugoinot relations are modified due to the presence of
chiral transport phenomena. We show that the entropy discontinuity in a weak
shock wave is quadratic in the pressure discontinuity when the effect of chiral
transport becomes sufficiently large. We also show that rarefaction shock
waves, which do not exist in usual nonchiral fluids, can appear in chiral
matter. The direction of shock wave propagation in a vorticity is found to be
completely determined by the direction of the vorticity and the chirality of
fermions. These features are exemplified by shock propagation in dense neutrino
matter in the hydrodynamic regime.
