We consider a one-dimensional nonlinear Schrodinger equation, modeling a Bose-Einstein condensate in an infinite square-well potential (box). This is a nonlinear control system in which the state is the wave function of the Bose-Einstein condensate and the control is the length of the box. We prove that local exact controllability around the ground state (associated with a fixed length of the box) holds generically with respect to the chemical potential mu, i.e., up to an at most countable set of mu-values. The proof relies on the linearization principle and the inverse mapping theorem, as well as ideas from analytic perturbation theory.