We report far-infrared and submillimeter observations of Supernova 1987A, the star that exploded on 23 February 1987 in the Large Magellanic Cloud, a galaxy located 160,000 light years away. The observations reveal the presence of a population of cold dust grains radiating with a temperature of about 17 to 23 K at a rate of about 220 L⊙. The intensity and spectral energy distribution of the emission suggests a dust mass of about 0.4 to 0.7 M⊙. The radiation must originate from the supernova ejecta and requires the efficient precipitation of all refractory material into dust. Our observations imply that supernovae can produce the large dust masses detected in young galaxies at very high redshifts.