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.