  We report anomalous circularly polarized Raman spectra of phonons in right-
and left-handed quartzes. The phonon branches splitting from the E-mode at a
finite wavenumber were found to be chiral with mutually opposite angular
momenta. Our analysis reveals the Raman selection rules for chiral phonons. We
also find that the conservation of angular momentum should be satisfied between
two photons and one chiral phonon in the Raman process. Furthermore, we
experimentally proved that the helicity of phonons with a certain frequency and
wavevector should be opposite in the other enantiomer.
