Expansions of short nucleotide repeats produce several neurological and neuromuscular disorders including Huntington disease, muscular dystrophy, and amyotrophic lateral sclerosis. A common pathological feature of these diseases is the accumulation of the repeat-containing transcripts into aberrant foci in the nucleus. RNA foci, as well as the disease symptoms, only manifest above a critical number of nucleotide repeats, but the molecular mechanism governing foci formation above this characteristic threshold remains unresolved. Here we show that repeat expansions create templates for multivalent base-pairing, which causes purified RNA to undergo a sol-gel transition in vitro at a similar critical repeat number as observed in the diseases. In human cells, RNA foci form by phase separation of the repeat-containing RNA and can be dissolved by agents that disrupt RNA gelation in vitro. Analogous to protein aggregation disorders, our results suggest that the sequence-specific gelation of RNAs could be a contributing factor to neurological disease.