For the first time the differential cross section for the elastic neutron-triton (n-(3)H) and neutron-deuteron (n-(2)H) scattering at 14.1 MeV has been measured by using an inertial confinement fusion facility. In these experiments, which were carried out by simultaneously measuring elastically scattered (3)H and (2)H ions from a deuterium-tritium gas-filled inertial confinement fusion capsule implosion, the differential cross section for the elastic n-(3)H scattering was obtained with significantly higher accuracy than achieved in previous accelerator experiments. The results compare well with calculations that combine the resonating-group method with an ab initio no-core shell model, which demonstrate that recent advances in ab initio theory can provide an accurate description of light-ion reactions.