Tumors comprise functionally diverse subpopulations of cells with distinct proliferative potential. Here, we show that dynamic epigenetic states defined by the linker histone H1.0 determine which cells within a tumor can sustain the long-term cancer growth. Numerous cancer types exhibit high inter-and intratumor heterogeneity of H1.0, with H1.0 levels correlating with tumor differentiation status, patient survival, and, at the single-cell level, cancer stem cell markers. Silencing of H1.0 promotes maintenance of self-renewing cells by inducing derepression of megabase-sized gene domains harboring downstream effectors of oncogenic pathways. Self-renewing epigenetic states are not stable, and reexpression of H1.0 in subsets of tumor cells establishes transcriptional programs that restrict cancer cells' long-term proliferative potential and drive their differentiation. Our results uncover epigenetic determinants of tumor-maintaining cells.