  Models of inflation involving non-Abelian gauge field backgrounds can produce
gravitational waves at an observable level with a preferred handedness. This
asymmetry comes about because the non-Abelian background generates
parity-violation in the action for perturbations. In the specific model we
study, Chromo-Natural Inflation, these gravitational waves can be produced at
observable levels even when no field makes a super-Planckian field excursion,
thus evading a common formulation of the Lyth bound. Unfortunately, when
considered in concert with the scalar fluctuations, this chiral enhancement of
the gravitational waves makes the model observationally inviable.
