A g-ray telescope using the double Compton process is described, which measures extraterrestrial g-ray fluxes in the energy range 1-10 MeV. The detector consists of 2 large plastic scintillator blocks, 1.20 m apart. A g-ray event is identified by a Compton collision crystal, the sequence being verified by a time-of-flight measurement. The properties of the telescope were measured in the lab. using the g-ray sources 60Co and 24Na. The telescope has an energy resoln. of +-20% and an abs. detection efficiency of .apprx.0.5%. Also, it has an esp. low sensitivity to undesired background g-rays. A slightly modified version of the telescope will be used in balloon flights to measure the spectrum of diffuse primary g-rays.