  We calculate the trispectrum of curvature perturbations for a model of
inflation endowed with Galilean symmetry at the level of the fluctuations
around an FRW background. Such a model has been shown to posses desirable
properties such as unitarity (up to a certain scale) and non-renormalization of
the leading operators, all of which point towards the reasonable assumption
that a full theory whose fluctuations reproduce the one here might exist as
well as be stable and predictive. The cubic curvature fluctuations of this
model produce quite distinct signatures at the level of the bispectrum. Our
analysis shows how this holds true at higher order in perturbations. We provide
a detailed study of the trispectrum shape-functions in different configurations
and a comparison with existent literature. Most notably, predictions markedly
differ from their P(X,\phi) counterpart in the so called equilateral
trispectrum configuration. The zoo of inflationary models characterized by
somewhat distinctive predictions for higher order correlators is already quite
populated; what makes this model more compelling resides in the above mentioned
stability properties.
