The spatial organization of chromosomes has key functional roles, yet how chromosomes fold remains poorly understood at the single-molecule level. Here, we employ models of polymer physics to investigate DNA loci in human HCT116 and IMR90 wild-type and cohesin depleted cells. Model predictions on single-molecule structures are validated against single-cell imaging data, providing evidence that chromosomal architecture is controlled by a thermodynamics mechanism of polymer phase separation whereby chromatin self-assembles in segregated globules by combinatorial interactions of chromatin factors that include CTCF and cohesin. The thermodynamics degeneracy of single-molecule conformations results in broad structural and temporal variability of TAD-like contact patterns. Globules establish stable environments where specific contacts are highly favored over stochastic encounters. Cohesin depletion reverses phase separation into randomly folded states, erasing average interaction patterns. Overall, globule phase separation appears to be a robust yet reversible mechanism of chromatin organization where stochasticity and specificity coexist.