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.
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