Cells respond to cellular stress by forming stress granules, molecular condensates containing non-translating messenger ribonucleoproteins. Stress granules form during chemotherapy and promote cell survival and chemoresistance, although the mechanism of this effect is not understood. We provide several lines of evidence that stress granules enhance cell survival by promoting cellular quiescence. First, we see a correlation between spontaneous stress granule formation and cell-cycle exit under non-stress conditions. Second, cells deficient in proteins required for stress granule formation (G3BP1/2) are less likely to exit the cell cycle under non-stress, stress, and chemotherapeutic conditions. Third, rescuing stress granule formation in G3BP1/2 knockout cells restores the fraction of cycling cells to wild-type levels. Finally, cells with enhanced stress granule formation (ddx6 knockout cells) show an increased propensity to exit the cell cycle. These results suggest that stress granules are important regulators of cellular quiescence, which could enable the identification of new anti-chemoresistance therapies that target stress granules.