Because of the low-energy threshold and relatively large cross section of the 9Be(n,2n) reaction, beryllium is a very attractive neutron multiplier for some fast-neutron systems, such as those used in the production of fusion energy. But, tritium is also produced when beryllium is irradiated with 14-MeV neutrons emitted from the fusion of deuterium and tritium ions. Among the two exit channels of the 9Be(n,t)7Li reaction of ~14-MeV incident-neutron energy, the 9Be(n,t1)7Li channel also emits a 0.478-MeV gamma ray. The purpose of the present study is to measure the cross section for the 9Be(n,t1)7Li reaction and also that of the more general 9Be(n,x)7Li reaction with the production of the same 0.478-MeV gamma ray for incident-neutron energies from the 12-MeV threshold to 200 MeV. Because the 7Li levels excited above 0.478 MeV are unstable against particle emission, the study of the 9Be(n,t1)7Li reaction gives direct access to the cross section for the formation of 7Li* in its 0.478-MeV excited state. The few previous experimental data for this reaction are restricted to incident-neutron energies of ~14 MeV with large discrepancies between the results. The present data are obtained with a BeO sample, using the pulsed source of high-energy neutrons of the Weapons Neutron Research Facility (WNR) at the Los Alamos Neutron Science Center (LANSCE). The 478-keV gamma rays emitted in 9Be(n,x)7Li reactions are detected with two high-resolution Ge detectors. The data thus obtained are presented and compared with previous data on the 9Be(n,t1)7Li and the 9Be(n,t)7Li reactions. Examination of the present data also provides insight into the 10Be level scheme.