Liquid–liquid phase separation is a major mechanism of subcellular compartmentalization^,. Although the segregation of RNA into phase-separated condensates broadly affects RNA metabolism^,, whether and how specific RNAs use phase separation to regulate interacting factors such as RNA-binding proteins (RBPs), and the phenotypic consequences of such regulatory interactions, are poorly understood. Here we show that RNA-driven phase separation is a key mechanism through which a long noncoding RNA (lncRNA) controls the activity of RBPs and maintains genomic stability in mammalian cells. The lncRNA NORAD prevents aberrant mitosis by inhibiting Pumilio (PUM) proteins^{, , –}. We show that NORAD can out-compete thousands of other PUM-binding transcripts to inhibit PUM by nucleating the formation of phase-separated PUM condensates, termed NP bodies. Dual mechanisms of PUM recruitment, involving multivalent PUM–NORAD and PUM–PUM interactions, enable NORAD to competitively sequester a super-stoichiometric amount of PUM in NP bodies. Disruption of NORAD-driven PUM phase separation leads to PUM hyperactivity and genome instability that is rescued by synthetic RNAs that induce the formation of PUM condensates. These results reveal a mechanism by which RNA-driven phase separation can regulate RBP activity and identify an essential role for this process in genome maintenance. The repetitive sequence architecture of NORAD and other lncRNAs^{, –} suggests that phase separation may be a widely used mechanism of lncRNA-mediated regulation.