All spectra measured with the High Energy resolution Gamma-Ray Spectroscopy Experiment (HEAO C-1) on the third High Energy Astronomy Observatory (HEAO 3) contain a strong line at 511 keV resulting from positron annihilation. This line originates in the instrument itself, the earth's atmosphere, and cosmic sources, possibly including the diffuse cosmic background. In order to understand the emission from cosmic sources, the atmospheric positron annihilation line emission has been determined as a function of geomagnetic latitude and zenith angle. Although the intensity of the line increases with increasing latitude, it was found that variations with zenith angle can be satisfactorily explained only if the atmospheric emission exhibits significant limb darkening. The atmospheric line has an energy of 511.07¿0.10 keV and a net width of 2.29¿0.30 keV FWHM. Characteristics of the instrument background have allowed an upper limit of 9.4¿10-3 photons/cm2-sec-sr to be placed on any narrow (≲3 keV) diffuse cosmic emission at 511 keV.