Tumor suppressor genes (TSGs) are essential for normal cellular function in multicellular organisms, but many TSGs and tumor-suppressing mechanisms remain unknown. Planarian flatworms exhibit particularly robust tumor suppression, yet the specific mechanisms underlying this trait remain unclear. Here, we analyze histone H3 lysine 4 trimethylation (H3K4me3) signal across the planarian genome to determine if the broad H3K4me3 chromatin signature that marks essential cell identity genes and TSGs in mammalian cells is conserved in this valuable model of in vivo stem cell function. We find that this signature is indeed conserved on the planarian genome and that the lysine methyltransferase Set1 is largely responsible for creating it at both cell identity and putative TSG loci. In addition, we show that depletion of in planarians induces stem cell phenotypes that suggest loss of TSG function, including hyperproliferation and an abnormal DNA damage response (DDR). Importantly, this work establishes that Set1 targets specific gene loci in planarian stem cells and marks them with a conserved chromatin signature. Moreover, our data strongly suggest that Set1 activity at these genes has important functional consequences both during normal homeostasis and in response to genotoxic stress.