We investigated the transcriptome of esophageal squamous cell carcinoma (ESCC) cells, activity of gene regulatory (enhancer and promoter regions), and the effects of blocking epigenetic regulatory proteins. We performed chromatin immunoprecipitation sequencing with antibodies against H3K4me1, H3K4me3, and H3K27ac and an assay for transposase-accessible chromatin to map the enhancer regions and accessible chromatin in 8 ESCC cell lines. We used the CRC_Mapper algorithm to identify core regulatory circuitry transcription factors in ESCC cell lines, and determined genome occupancy profiles for 3 of these factors. In ESCC cell lines, expression of transcription factors was knocked down with small hairpin RNAs, promoter and enhancer regions were disrupted by CRISPR/Cas9 genome editing, or bromodomains and extraterminal (BET) family proteins and histone deacetylases (HDACs) were inhibited with ARV-771 and romidepsin, respectively. ESCC cell lines were then analyzed by whole-transcriptome sequencing, immunoprecipitation, immunoblots, immunohistochemistry, and viability assays. Interactions between distal enhancers and promoters were identified and verified with circular chromosome conformation capture sequencing. NOD-SCID mice were given injections of modified ESCC cells, some mice where given injections of HDAC or BET inhibitors, and growth of xenograft tumors was measured. We identified super-enhancer-regulated circuits and transcription factors TP63, SOX2, and KLF5 as core regulatory factors in ESCC cells. Super-enhancer regulation of ALDH3A1 mediated by core regulatory factors was required for ESCC viability. We observed direct interactions between the promoter region of TP63 and functional enhancers, mediated by the core regulatory circuitry transcription factors. Deletion of enhancer regions from ESCC cells decreased expression of the core regulatory circuitry transcription factors and reduced cell viability; these same results were observed with knockdown of each core regulatory circuitry transcription factor. Incubation of ESCC cells with BET and HDAC disrupted the core regulatory circuitry program and the epigenetic modifications observed in these cells; mice given injections of HDAC or BET inhibitors developed smaller xenograft tumors from the ESCC cell lines. Xenograft tumors grew more slowly in mice given the combination of ARV-771 and romidepsin than mice given either agent alone. In epigenetic and transcriptional analyses of ESCC cell lines, we found the transcription factors TP63, SOX2, and KLF5 to be part of a core regulatory network that determines chromatin accessibility, epigenetic modifications, and gene expression patterns in these cells. A combination of epigenetic inhibitors slowed growth of xenograft tumors derived from ESCC cells in mice.