We probe the local electronic structure at solvated Na+ ions in 1 M aqueous NaCl solutions as a function of pH. A dramatic change in the Na+ white line intensity in X-ray absorption is observed for high pH values, reflecting a changing local electronic structure at the Na+ ions when OH- is present. Given the relative abundance of sodium and hydroxide ions, we conclude that one OH- affects at least 2.4+/-0.6 Na+ ions in an electronically noticeable way at pH 13. From the experimental data we infer that spatially extended clusters or networks incorporating Na+ and OH- can exist in the electrolyte solution. The experimental data are complemented by molecular dynamics simulations, which indicate the presence of structured clusters incorporating Na+, OH-, and solvent molecules.