In the last quarter of the 20th century, studies with a number of model systems produced a hypothesis that the higher eukaryotic genome consists of functionally isolated areas termed genomic domains. Each domain includes one or more genes and a regulatory system that is normally active only for the given domain and allows it to achieve a regulatory autonomy of the neighboring chromosome regions. A genome domain is characterized by spectra of covalent histone modifications, which determine the domain boundaries and the extent of chromatin condensation within the domain, thus determining whether transcriptional activation is possible for the domain genes. The domain hypothesis of genome organization is due, to a large extent, to studies of the mechanisms regulating transcription of the globin genes in vertebrates. The chicken β-globin gene domain is one of the most popular models in the field. The model was used to investigate the basic principles of the complex function of higher eukaryotic enhancers, the properties of insulators and functional units of eukaryotic enhancers and promoters, the influence of covalent histone modifications on the extent of chromatin condensation, and the role of such modifications in regulating transcription within the domain. The review summarizes the data on the chicken β-globin gene domain and considers the domain hypothesis of eukaryotic genome organization.