An experimental measurement of the spectrum of the submillimeter cosmic background radiation is described. The experiment consists of measuring the night sky emission at an altitude of 39 km, correcting for the atmospheric molecular line emission, and placing limits on the contamination from sources of continuum radiation such as the apparatus itself and the earth. The observations were made on 24 July 1974 using a fully calibrated liquid-helium-cooled balloon- borne spectrophotometer. Important features of the apparatus include a cooled antenna, a polarizing interferometer, and a germanium bolometric detector. The characterization of the spectrophotometer includes the large angle response and emission of the antenna. The calibration of the instrument and corrections to the observed sky spectrum are based on measurements made during the flight. A simple model of the molecular line emission is used to determine the atmospheric contribution. The resulting spectrum covers the frequency range from 4 to 17 cm$sup -1$ and establishes that the cosmic background radiation follows the high frequency quantum cutoff for a 3K blackbody. A blackbody temperature of 2.99/sub -.$sub 14$/$sup +$.$sup 07$/K is deduced from our data. The present status of the cosmic background observations, which span more than three decades in frequency, is analyzed …