Epigenetics, or the reversible and heritable marks of gene regulation not including DNA sequence, encompasses chromatin modifications on both the DNA and histones and is as important as the DNA sequence itself. Chromatin-modifying factors are playing an increasingly important role in tumorigenesis, particularly among pediatric rhabdomyosarcomas (RMS), revealing potential novel therapeutic targets. We performed an overexpression screen of chromatin-modifying factors in a KRASG12D-driven zebrafish model for RMS. Here, we describe the identification of a histone H3 lysine 9 histone methyltransferase, SUV39H1, as a suppressor of embryonal RMS formation in zebrafish. This suppression is specific to the histone methyltransferase activity of SUV39H1, as point mutations in the SET domain lacked the effect. SUV39H1-overexpressing and control tumors have a similar proliferation rate, muscle differentiation state, and tumor growth rate. Strikingly, SUV39H1-overexpressing fish initiate fewer tumors, which results in the observed suppressive phenotype. We demonstrate that the delayed tumor onset occurs between 5 and 7 days post fertilization. Gene expression profiling at these stages revealed that in the context of KRASG12D overexpression, SUV39H1 may suppress cell cycle progression. Our studies provide evidence for the role of SUV39H1 as a tumor suppressor.