The Collaborative International Dictionary of English v.0.48:

Anadiplosis \An`a*di*plo"sis\, n. [L., fr. Gr. ?; ? + ? to
   double, ?, ?, twofold, double.] (Rhet.)
   A repetition of the last word or any prominent word in a
   sentence or clause, at the beginning of the next, with an
   adjunct idea; as, "He retained his virtues amidst all his
   misfortunes -- misfortunes which no prudence could foresee or
   prevent."
   [1913 Webster]

WordNet (r) 3.0 (2006):

anadiplosis
    n 1: repetition of the final words of a sentence or line at the
         beginning of the next [syn: anadiplosis, reduplication]