Synovial sarcoma (SyS) is an aggressive mesenchymal malignancy invariably associated with the chromosomal translocation t(X:18; p11:q11), which results in the in-frame fusion of the BAF complex gene SS18 to one of three SSX genes. Fusion of SS18 to SSX generates an aberrant transcriptional regulator, which, in permissive cells, drives tumor development by initiating major chromatin remodeling events that disrupt the balance between BAF-mediated gene activation and polycomb-dependent repression. Here, we developed SyS organoids and performed genome-wide epigenomic profiling of these models and mesenchymal precursors to define SyS-specific chromatin remodeling mechanisms and dependencies. We show that SS18-SSX induces broad BAF domains at its binding sites, which oppose polycomb repressor complex (PRC) 2 activity, while facilitating recruitment of a non-canonical (nc)PRC1 variant. Along with the uncoupling of polycomb complexes, we observed H3K27me3 eviction, H2AK119ub deposition and the establishment of de novo active regulatory elements that drive SyS identity. These alterations are completely reversible upon SS18-SSX depletion and are associated with vulnerability to USP7 loss, a core member of ncPRC1.1. Using the power of primary tumor organoids, our work helps define the mechanisms of epigenetic dysregulation on which SyS cells are dependent.