  We study the ground state of a large bosonic system trapped in a symmetric
double-well potential, letting the distance between the two wells increase to
infinity with the number of particles. In this context, one should expect an
interaction-driven transition between a delocalized state (particles are
independent and all live in both wells) and a localized state (particles are
correlated, half of them live in each well). We start from the full many-body
Schr{\"o}dinger Hamiltonian in a large-filling situation where the on-site
interaction and kinetic energies are comparable. When tunneling is negligible
against interaction energy, we prove a localization estimate showing that the
particle number fluctuations in each well are strongly suppressed. The modes in
which the particles condense are minimizers of nonlinear Schr{\"o}dinger-type
functionals.
