This article shows that endoclitics do exist in Udi, a language of the North East Caucasian family, and this fact poses a challenge to the lexicalist hypothesis. Clitics may be positioned between the morphemes of complex verb stems and immediately before the final segments of monomorphemic verb stems. The author argues, on the basis of accepted tests for wordhood, that complex verb stems are single words, not phrases. On the basis of criteria developed by Zwicky and Pullum (1983), it is argued that the clitics of Udi are true clitics. An analysis of the placement of clitics in various positions inside verb stems is proposed in optimality theory. The author shows that phonological phenomena do not provide an alternative basis for positioning these clitics and concludes that clitics in Udi are a counterexample to the lexical integrity hypothesis.