Prebiotic molecules derive from abiotic organic molecules, radicals, and ions that pervade the universe at temperatures as high as several 1000 K. Here we review the role of organic molecules that condensed at low temperatures before or during comet formation in the early history of the Solar System. Recent spacecraft encounters and ground-based observations of carbon-rich volatile and dust components of comet comae provide a broad database for the investigation of these organic molecules. New laboratory data for some potential cometary organics are presented. Probable icy organic constituents of the nucleus and CHON particles as likely candidates for the distributed sources of gas-phase organic species in the coma are discussed. There is broad agreement that many organic molecules observed in the coma originate from the dust that must have existed in the solar nebula at the time and place of comet formation. We conclude that complex organic molecules found in comets may be a source of prebiotic molecules that led to the origins of life.