  The results in this paper are in a context of abstract elementary classes
identified by Shelah and Villaveces in which the amalgamation property is not
assumed. The long-term goal is to solve Shelah's Categoricity Conjecture in
this context. Here we tackle a problem of Shelah and Villaveces by proving that
in their context, the uniqueness of limit models follows from categoricity
under the assumption that the subclass of amalgamation bases is closed under
unions of bounded, increasing chains.
