SignificancePredicting how epigenetic marks control the 3D organization of the genome is key to understanding how these marks regulate gene expression. We show that a physical model of a chromosome with experimentally measured local interactions segregates into euchromatin- and heterochromatin-like phases. The model reproduces many of the features of the large-scale organization of the chromosome as measured by Hi-C. Our work provides an estimate of the amount of epigenetic marking needed to segregate a gene into heterochromatin.