The enteric nervous system (ENS) consists of glial cells (EGCs) and neurons derived from neural crest precursors. EGCs retain capacity for large-scale neurogenesis in culture, and in vivo lineage tracing has identified neurons derived from glial cells in response to inflammation. We thus hypothesize that EGCs possess a chromatin structure poised for neurogenesis. We use single-cell multiome sequencing to simultaneously assess transcription and chromatin accessibility in EGCs undergoing spontaneous neurogenesis in culture, as well as small intestine myenteric plexus EGCs. Cultured EGCs maintain open chromatin at genomic loci accessible in neurons, and neurogenesis from EGCs involves dynamic chromatin rearrangements with a net decrease in accessible chromatin. A subset of in vivo EGCs, highly enriched within the myenteric ganglia and that persist into adulthood, have a gene expression program and chromatin state consistent with neurogenic potential. These results clarify the mechanisms underlying EGC potential for neuronal fate transition.