The formation of a dineutron in the Li-11 nucleus is found to be localized to the surface region. The experiment measured the intrinsic momentum of the struck neutron in Li-11 via the op; pnTHORN knockout reaction at 246 MeV=nucleon. The correlation angle between the two neutrons is, for the first time, measured as a function of the intrinsic neutron momentum. A comparison with reaction calculations reveals the localization of the dineutron at r similar to 3.6 fm. The results also support the density dependence of dineutron formation as deduced from Hartree-Fock-Bogoliubov calculations for nuclear matter.