Chimeric transcription factors drive lineage-specific oncogenesis but are notoriously difficult to target. Alveolar rhabdomyosarcoma (RMS) is an aggressive childhood soft tissue sarcoma transformed by the pathognomonic Paired Box 3–Forkhead Box O1 (PAX3-FOXO1) fusion protein, which governs a core regulatory circuitry transcription factor network. Here, we show that the histone lysine demethylase 4B (KDM4B) is a therapeutic vulnerability for PAX3-FOXO1 ⁺ RMS. Genetic and pharmacologic inhibition of KDM4B substantially delayed tumor growth. Suppression of KDM4 proteins inhibited the expression of core oncogenic transcription factors and caused epigenetic alterations of PAX3-FOXO1–governed superenhancers. Combining KDM4 inhibition with cytotoxic chemotherapy led to tumor regression in preclinical PAX3-FOXO1 ⁺ RMS subcutaneous xenograft models. In summary, we identified a targetable mechanism required for maintenance of the PAX3-FOXO1–related transcription factor network, which may translate to a therapeutic approach for fusion-positive RMS.