We consider a Bose gas consisting of N particles in \mathbb{R}^3, trapped by an external field and interacting through a two-body potential with scattering length of order N^{-1}. We prove that low energy states exhibit complete Bose-Einstein condensation with optimal rate, generalizing previous work in \cite{BBCS1, BBCS4}, restricted to translation invariant systems. This extends recent results in \cite{NNRT}, removing the smallness assumption on the size of the scattering length.
