We present the first neutron diffraction studies of the structure of lithium-methylamine solutions as they cross the metal-nonmetal transition. A shift in the principle scattering peak immediately reflects the overall decrease in density as the solvent expands to accommodate the excess electrons. Li-6/Li-7 isotopic labeling then allows us to answer key questions concerning cation solvation. We find that each lithium cation is coordinated to four methylamine molecules. However, the cation solvation shell expands as the system becomes metallic: a direct structural signature of electron delocalization. As a result of correlations between strongly solvated lithium ions, the solutions are highly structured over intermediate length scales. The valence electrons then reside primarily in polaronic cavities, formed by the solvated cations and remaining solvent molecules.