Genome-wide hypertranscription is common in human cancer and predicts poor prognosis. To understand how hypertranscription might drive cancer, we applied our FFPE-CUTAC method for mapping RNA Polymerase II (RNAPII) genome-wide in formalin-fixed paraffin-embedded (FFPE) sections. We demonstrate global RNAPII elevations in mouse gliomas and assorted human tumors in small clinical samples and discover regional elevations corresponding to HER2 amplifications punctuated by likely selective sweeps. RNAPII occupancy at replication-coupled histone genes correlated with WHO grade in meningiomas, accurately predicted rapid recurrence, and corresponded to whole-arm chromosome losses. Elevated RNAPII at histone genes in meningiomas and diverse breast cancers is consistent with histone production being rate-limiting for S-phase progression and histone gene hypertranscription driving overproliferation and aneuploidy in cancer, with general implications for precision oncology.