  Galileon inflation is a radiatively stable higher derivative model of
inflation. The model is determined by a finite number of relevant operators
which are protected by a covariant generalization of the Galileon shift
symmetry. We show that the nongaussianity of the primordial density
perturbation generated during an epoch of Galileon inflation is a particularly
powerful observational probe of these models and that, when the speed of sound
is small, fNL can be larger than the usual result fNL ~ 1/c_s^2.
