  We investigate the viability of inflation with a spectator sector comprised
of non-Abelian gauge fields coupled through a higher order operator. We dub
this model "spectator Gauge-flation". We study the predictions for the
amplitude and tensor tilt of chiral gravitational waves and conclude that a
slightly red-tilted tensor power spectrum is preferred $n_T=-{\cal O}(0.01)$.
As with related models, the enhancement of chiral gravitational waves with
respect to the single-field vacuum gravitational wave background is controlled
by the parameter $\gamma=g^2 Q^2/H^2$, where $g$ is the gauge coupling, $H$ is
the Hubble scale and $Q$ is the VEV of the $SU(2)$ sector. The requirement that
the $SU(2)$ is a spectator sector leads to a maximum allowed value for
$\gamma$, thereby constraining the possible amplification. In order to provide
concrete predictions, we use an $\alpha$-attractor T-model potential for the
inflaton sector. Potential observation of chiral gravitational waves with
significantly tilted tensor spectra would then indicate the presence of
additional couplings of the gauge fields to axions, like in the spectator
axion-SU(2) model, or additional gauge field operators.
