Evidence for superconductivity in the organic conductor di-(tetramethyltetraselenafulvalenium)-perchlorate [(TMTSF)2ClO4] has been found by resistance measurements in the absence of applied pressure. For different crystals the transitions are approximately 0.3 K wide and are centered around temperatures between 1.2 and 1.4 K. At 0.9 K, a perpendicular magnetic field of 25 mT nearly restores normal resistance. Below 0.1 K, this critical field exceeds 50 mT.