The three-dimensional structure of the genome is an important regulator of many cellular processes including differentiation and gene regulation. Recently, technologies such as Hi-C that combine proximity ligation with high-throughput sequencing have revealed domains of self-interacting chromatin, called topologically associating domains (TADs), in many organisms. Current methods for identifying TADs using Hi-C data assume that TADs are non-overlapping, despite evidence for a nested structure in which TADs and sub-TADs form a complex hierarchy. We introduce a model for decomposition of contact frequencies into a hierarchy of nested TADs. This model is based on empirical distributions of contact frequencies within TADs, where positions that are far apart have a greater enrichment of contacts than positions that are close together. We find that the increase in contact enrichment with distance is stronger for the inner TAD than for the outer TAD in a TAD/sub-TAD pair. Using this model, we develop the TADtree algorithm for detecting hierarchies of nested TADs. TADtree compares favorably with previous methods, finding TADs with a greater enrichment of chromatin marks such as CTCF at their boundaries. A python implementation of TADtree is available at http://compbio.cs.brown.edu/software/ braphael@cs.brown.edu Supplementary data are available at Bioinformatics online.