We report here measurements of the terrestrial and extraterrestrial 0.511-MeV gamma rays with a collimated high-resolution gamma ray spectrometer which was flown on a balloon over Palestine, Texas, on June 10, 1974. The instrument consists of four 40-cm3 Ge(Li) crystals surrounded by a Csl(Na) shield. The angular resolution of the instrument is 30¿ full width at half maximum, and the energy resolution is 2.3 keV at 0.511 MeV. Our measurements of the atmospheric fluxes are consistent with reported fluxes measured with omnidirectional scintillaion detectors and with angular distributions and depth variations of the intensities drived from a semiempirical model after allowance is made for a component of the background rate due to B+ decays produced by neutron- and proton-initiated interactions with materials near the detectors. Our 2&sgr; upper-limit measurement of the cosmic diffuse flux from the galactic anticenter direction is 9.2¿10-3 photon/(cm2 s sr), and the 2 &sgr; upper-limit flux from the Crab Nebular and the quiet sun at the top of the atmosphere is 4.6¿10-3 photon/(cm2 s).