Accumulating evidence implicates heterogeneity within cancer cell populations in the response to stressful exposures, including drug treatments. While modeling the acute response to various anticancer agents in drug-sensitive human tumor cell lines, we consistently detected a small subpopulation of reversibly "drug-tolerant" cells. These cells demonstrate >100-fold reduced drug sensitivity and maintain viability via engagement of IGF-1 receptor signaling and an altered chromatin state that requires the histone demethylase RBP2/KDM5A/Jarid1A. This drug-tolerant phenotype is transiently acquired and relinquished at low frequency by individual cells within the population, implicating the dynamic regulation of phenotypic heterogeneity in drug tolerance. The drug-tolerant subpopulation can be selectively ablated by treatment with IGF-1 receptor inhibitors or chromatin-modifying agents, potentially yielding a therapeutic opportunity. Together, these findings suggest that cancer cell populations employ a dynamic survival strategy in which individual cells transiently assume a reversibly drug-tolerant state to protect the population from eradication by potentially lethal exposures.