The theory of the liquid-glass transition is extended to describe the polymerization of RNA in a nucleotide-condensed state. In the glassy state the ribose subunits are joined by a 2'-5' or 3'-5' phosphodiester linkage to form the ribose-phosphate backbone similar to oligosaccharides and polysaccharides. The occurrence of the glass transition requires two conditions: (1) a supercooled state in a nucleotide-condensed state should exist below the temperature at which the whole RNA hydrolyzes; (2) the Gibbs free energy due to the Kauzmann entropy, which obeys a Curie law with a negative sign, must be larger than the height of the potential barrier for nucleotides to overcome to form the binding.