The three-dimensional configuration of DNA is integral to all nuclear processes in eukaryotes, yet our knowledge of the chromosome architecture is still limited. Genome-wide chromosome conformation capture studies have uncovered features of chromatin organization in cultured cells, but genome architecture in human tissues has yet to be explored. Here, we report the most comprehensive survey to date of chromatin organization in human tissues. Through integrative analysis of chromatin contact maps in 21 primary human tissues and cell types, we find topologically associating domains highly conserved in different tissues. We also discover genomic regions that exhibit unusually high levels of local chromatin interactions. These frequently interacting regions (FIREs) are enriched for super-enhancers and are near tissue-specifically expressed genes. They display strong tissue-specificity in local chromatin interactions. Additionally, FIRE formation is partially dependent on CTCF and the Cohesin complex. We further show that FIREs can help annotate the function of non-coding sequence variants.