The long genomic DNA molecules in eukaryotes are fragile and prone to entanglement, and must be tightly folded to fit into the micrometric dimensions of mitotic chromosomes. Histones transform the monotonous linear structure of double‐helical DNA into a chromatin filament formed by many nucleosomes. A physically consistent model for the packaging of the chromatin filament must be compatible with all the constraints imposed by the structural properties of chromosomes. It has to be compatible with 1) the high concentration of DNA and the elongated cylindrical shape of chromosomes and 2) the known self‐associative properties of chromatin, and also with 3) an effective protection of chromosomal DNA from topological entanglement and mechanical breakage. The multilayer chromosome model, in which a repetitive weak interaction between nucleosomes at the nanoscale produces the stacking of many chromatin layers, is compatible with all these constraints. The self‐organization of the multilayer structure of the whole chromosome is consistent with current knowledge of the self‐assembly of micrometric structures from different repetitive building blocks. The multilayer model justifies the geometry of chromosome bands and translocations, and is compatible with feasible physical mechanisms for the control of gene expression, and for DNA replication, repair, and segregation to daughter cells.