Glioblastoma, the most common and aggressive malignant brain tumor, is propagated by stem-like cancer cells refractory to existing therapies. Understanding the molecular mechanisms that control glioblastoma stem cell (GSC) proliferation and drug resistance may reveal opportunities for therapeutic interventions. Here we show that GSCs can reversibly transition to a slow-cycling, persistent state in response to targeted kinase inhibitors. In this state, GSCs upregulate primitive developmental programs and are dependent upon Notch signaling. This transition is accompanied by widespread redistribution of repressive histone methylation. Accordingly, persister GSCs upregulate, and are dependent on, the histone demethylases KDM6A/B. Slow-cycling cells with high Notch activity and histone demethylase expression are present in primary glioblastomas before treatment, potentially contributing to relapse. Our findings illustrate how cancer cells may hijack aspects of native developmental programs for deranged proliferation, adaptation, and tolerance. They also suggest strategies for eliminating refractory tumor cells by targeting epigenetic and developmental pathways.