  We show that an inflation model in which a spectator axion field is coupled
to an SU(2) gauge field produces a large three-point function (bispectrum) of
primordial gravitational waves, $B_{h}$, on the scales relevant to the cosmic
microwave background experiments. The amplitude of the bispectrum at the
equilateral configuration is characterized by
$B_{h}/P_h^2=\mathcal{O}(10)\times \Omega_A^{-1}$, where $\Omega_A$ is a
fraction of the energy density in the gauge field and $P_h$ is the power
spectrum of gravitational waves produced by the gauge field.
