The pluripotent state of embryonic stem cells (ESCs) is produced by active transcription of genes that control cell identity and repression of genes encoding lineage-specifying developmental regulators. Here, we use ESC cohesin ChIA-PET data to identify the local chromosomal structures at both active and repressed genes across the genome. The results produce a map of enhancer-promoter interactions and reveal that super-enhancer-driven genes generally occur within chromosome structures that are formed by the looping of two interacting CTCF sites co-occupied by cohesin. These looped structures form insulated neighborhoods whose integrity is important for proper expression of local genes. We also find that repressed genes encoding lineage-specifying developmental regulators occur within insulated neighborhoods. These results provide insights into the relationship between transcriptional control of cell identity genes and control of local chromosome structure.