  We compute the leading order contribution to the four-point function of the
primordial curvature perturbation in a class of single field models where the
inflationary Lagrangian is a general function of the inflaton and its first
derivative. This class of models includes string motivated inflationary models
such as DBI inflation. We find that the trispectrum for some range of
parameters could potentially be observed in future experiments. Moreover, the
trispectrum can distinguish DBI inflation from other inflation models with
large non-Gaussianities which typically have a similar bispectrum. We also
derive a set of consistency conditions for n-point functions of the primordial
curvature perturbation in single field inflation, generalizing Maldacena's
result for 3-point functions.
