  We report on a new mechanism that leads to the generation of primordial
chiral gravitational waves, and hence, the violation of the parity symmetry in
the Universe. We show that nonperturbative production of fermions with a
definite helicity is accompanied by the generation of chiral gravitational
waves. This is a generic and model-independent phenomenon that can occur during
inflation, reheating and radiation eras, and can leave imprints in the cosmic
microwave background polarization and may be observed in future ground- and
space-based interferometers. We also discuss a specific model where chiral
gravitational waves are generated via the production of light chiral fermions
during pseudoscalar inflation.
