  The linearized Einstein equation describing graviton propagation through a
chiral medium appears to be helicity dependent. We analyze features of the
corresponding spectrum in a collision-less regime above a flat background. In
the long wave-length limit, circularly polarized metric perturbations travel
with a helicity dependent group velocity that can turn negative giving rise to
a new type of an anomalous dispersion. We further show that this chiral
anomalous dispersion is a general feature of polarized modes propagating
through chiral plasmas extending our result to the electromagnetic sector.
