Three-dimensional genome organization is an important higher order transcription regulation mechanism that can be studied with the chromosome conformation capture techniques. Here, we combined chromatin organization analysis by chromosome conformation capture-carbon copy, computational modeling and epigenomics to achieve the first integrated view, through time, of a connection between chromatin state and its architecture. We used this approach to examine the chromatin dynamics of the HoxA cluster in a human myeloid leukemia cell line at various stages of differentiation. We found that cellular differentiation involves a transient activation of the 5'-end HoxA genes coinciding with a loss of contacts throughout the cluster, and by specific silencing at the 3'-end with H3K27 methylation. The 3D modeling of the data revealed an extensive reorganization of the cluster between the two previously reported topologically associated domains in differentiated cells. Our results support a model whereby silencing by polycomb group proteins and reconfiguration of CTCF interactions at a topologically associated domain boundary participate in changing the HoxA cluster topology, which compartmentalizes the genes following differentiation.