Although the importance of chromosome organization during mitosis is clear, it remains to be determined whether the nucleus assumes other functionally relevant chromosomal topologies. We have previously shown that homologous chromosomes have a tendency to associate during hematopoiesis according to their distribution of coregulated genes, suggesting cell-specific nuclear organization. Here, using the mathematical approaches of distance matrices and coupled oscillators, we model the dynamic relationship between gene expression and chromosomal associations during the differentiation of a multi-potential hematopoietic progenitor. Our analysis reveals dramatic changes in total genomic order: commitment of the progenitor results in an initial increase in entropy at both the level of gene co-regulation and chromosomal organization, which we suggest represents a phase transition, followed by a progressive decline in entropy during differentiation. The stabilization of a highly ordered state in the differentiated cell types results in lineage-specific chromosomal topologies and is related to the emergence of coherence—or self-organization—between chromosomal associations and coordinate gene regulation. We discuss how these observations may be generally relevant to cell fate decisions encountered by progenitor/stem cells.