  We give a method to construct singular Lagrangian 3-torus fibrations over
certain a priori given integral affine manifolds with singularities, which we
call simple. The main result of this article is the proof that the topological
Calabi-Yau compactifications of M. Gross' "Topological Mirror Symmetry", can be
made into symplectic compactifications. As an example, we obtain a pair of
compact symplectic 6-manifolds together with Lagrangian fibrations whose
underlying affine structures are dual. The symplectic manifolds obtained are
homeomorphic to a smooth quintic Calabi-Yau 3-fold and its mirror.
