The simplest elements, hydrogen and helium, offer a remarkably rich chemistry, which has controlled crucial features of the early evolution of the universe. Theoretical models of the origin of structure (stars, galaxies, clusters of galaxies, etc.) now incorporate this chemistry in some detail. In addition to the origin of structure, cosmologists are concerned with observational tests of competing world models. Primordial chemistry may give rise to some of the earliest departures from thermodynamic equilibrium in the universe. These effects may be observable as broad-band spectroscopic distortions of the cosmic background radiation, which otherwise exhibits a nearly perfect blackbody spectrum. The chemical history of the expanding universe is followed through a detailed calculation of the evolution of the abundances of H, H+, H-, H2, H2+, H3+, and other minor species. It is shown that continuous absorption by the small concentration of H- can produce a distortion in the cosmic background spectrum with a maximum at a frequency near nu/c = 9 cm-1 (wavelength 1.1 mm). The predicted effect lies only a factor of 5 below current limits. Its detection would provide an important test of our understanding of the recombination epoch of the universe.