We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as 80 cm;{-1} below the lowest ionization threshold. The density of excited molecules in the illuminated volume approaches 1x10;{13} cm;{-3}. This population evolves to produce free electrons and a durable cold plasma of electrons and intact NO+ ions.