  We calculate the bispectrum of scale-invariant tensor modes sourced by
spectator SU(2) gauge fields during inflation in a model containing a scalar
inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is
generated in this model at tree-level as the gauge fields contain a tensor
degree of freedom, and its production is dominated by self-coupling of the
gauge fields. This is a unique feature of non-Abelian gauge theory. The shape
of the tensor bispectrum is approximately an equilateral shape for $3\lesssim
m_Q\lesssim 4$, where $m_Q$ is an effective dimensionless mass of the SU(2)
field normalised by the Hubble expansion rate during inflation. The amplitude
of non-Gaussianity of the tensor modes, characterised by the ratio $B_h/P^2_h$,
is inversely proportional to the energy density fraction of the gauge field.
This ratio can be much greater than unity, whereas the ratio from the vacuum
fluctuation of the metric is of order unity. The bispectrum is effective at
constraining large $m_Q$ regions of the parameter space, whereas the power
spectrum constrains small $m_Q$ regions.
