We present a satellite observation of the spectrum of gamma radiation from the Earth's atmosphere in the energy interval from 300 keV to 8.5 MeV. The data were accumulated by the gamma ray spectrometer on the Solar Maximum Mission over 3 1/2 years, from 1980 to 1983. The excellent statistical accuracy of the data allows 20 atmospheric line features to be identified. The features are superimposed on a continuum background which is modeled using a power law with index -1.16. Many of these features contain a blend of more than one nuclear line. All of these lines (with the exception of the 511-keV annihilation line) are Doppler broadened. Line energies and intensities are consistent with production by secondary neutrons interacting with atmospheric 14N and 16O. Although we find no evidence for other production mechanisms, we cannot rule out significant contributions from direct excitation or spallation by primary cosmic ray protons. The relative intensities of the observed line features are in fair agreement with theoretical models; however, existing models are limited by the availability of neutron cross sections, especially at high energies. The intensity and spectrum of photons at energies below the 511-keV line, in excess of a power law continuum, can be explained by Compton scattering of the annihilation line photons in traversing an average of approximately 21 g cm-2 of atmosphere.