Recent studies involving the 3-dimensional conformation of chromatin have revealed the important role it has to play in different processes within the cell. These studies have also led to the discovery of densely interacting segments of the chromosome, called topologically associating domains. The accurate identification of these domains from Hi-C interaction data is an interesting and important computational problem for which numerous methods have been proposed. Unfortunately, most existing algorithms designed to identify these domains assume that they are non-overlapping whereas there is substantial evidence to believe a nested structure exists. We present a methodology to predict hierarchical chromatin domains using chromatin conformation capture data. Our method predicts domains at different resolutions, calculated using intrinsic properties of the chromatin data, and effectively clusters these to construct the hierarchy. At each individual level, the domains are non-overlapping in such a way that the intra-domain interaction frequencies are maximized. We show that our predicted structure is highly enriched for actively transcribing housekeeping genes and various chromatin markers, including CTCF, around the domain boundaries. We also show that large-scale domains, at multiple resolutions within our hierarchy, are conserved across cell types and species. We also provide comparisons against existing tools for extracting hierarchical domains. Our software, Matryoshka, is written in C++11 and licensed under GPL v3; it is available at https://github.com/COMBINE-lab/matryoshka.