  We calculate the trispectrum of the primordial curvature perturbation
generated by an epoch of slow-roll inflation in the early universe, and
demonstrate that the non-gaussian signature imprinted at horizon crossing is
unobservably small, of order tau_NL < r/50, where r < 1 is the tensor-to-scalar
ratio. Therefore any primordial non-gaussianity observed in future microwave
background experiments is likely to have been synthesized by gravitational
effects on superhorizon scales. We discuss the application of Maldacena's
consistency condition to the trispectrum.
