We have detected Lyman alpha radiation, 121.6 nm light produced from the n = 2 to n = 1 transition in atomic hydrogen, as a product of the He-3 (n, tp) nuclear reaction occurring in a cell of He-3 gas. The predominant source of this radiation appears to be decay of the 2p state of tritium produced by charge transfer and excitation collisions with the background He-3 gas. Under the experimental conditions reported here we find yields of tens of Lyman alpha photons for every neutron reaction. These results suggest a method of cold neutron detection that is complementary to existing technologies that use proportional counters. In particular, this approach may provide single neutron sensitivity with wide dynamic range capability, and a class of neutron detectors that are compact and operate at relatively low voltages.