  We prove that if X is a locally complete intersection variety, then X has all
the jet schemes irreducible if and only if X has canonical singularities. After
embedding X in a smooth variety Y, we use motivic integration to express the
condition that X has irreducible jet schemes in terms of data coming from an
embedded resolution of X in Y. We show that this condition is equivalent with
having canonical singularities. In the appendix, this result is used to prove a
generalization of Kostant's freeness theorem to the setting of jet schemes.
