Acute Myeloid Leukemia (AML) is an aggressive hematological malignancy with abnormal progenitor self-renewal and defective white blood cell differentiation. Its pathogenesis comprises subversion of transcriptional regulation, through mutation and by hijacking normal chromatin regulation. Kat2a is a histone acetyltransferase central to promoter activity, that we recently associated with stability of pluripotency networks, and identified as a genetic vulnerability in AML. Through combined chromatin profiling and single-cell transcriptomics of a conditional knockout mouse, we demonstrate that Kat2a contributes to leukemia propagation through preservation of leukemia stem-like cells. Kat2a loss impacts transcription factor binding and reduces transcriptional burst frequency in a subset of gene promoters, generating enhanced variability of transcript levels. Destabilization of target programs shifts leukemia cell fate out of self-renewal into differentiation. We propose that control of transcriptional variability is central to leukemia stem-like cell propagation, and establish a paradigm exploitable in different tumors and distinct stages of cancer evolution.