Chromatin packaging in eukaryotic chromosomes has been traditionally viewed as a hierarchical process, in which nucleosome chains fold into helical chromatin fibers. These fibers would then fold into more complex coiled structures. However, recent chromatin imaging studies and analyses of DNA contacts within the 3D space of the cell nucleus have necessitated a radical revision of the hierarchical chromatin packing model. According to the new studies, the nucleosome chain has a heteromorphic spatial configuration forming no regular helical fibers in most cell types and the higher-order chromatin folding in the cell nucleus leads to formation of distinct DNA contact domains of up to several million base pairs in size. Our previous studies revealed that during cell differentiation, individual epigenetically modified chromatin domains marked by certain types of histone modifications can merge together and form chromosomal sub-compartments suited for local gene activation or repression. This “attraction of likeness” may be driven by direct self-association of nucleosome chains mediated by histone N-tails as well as by architectural chromatin proteins making oligomeric protein “bridges” between nucleosomes; both eventually leading to liquid-liquid phase separation inside the cell nucleus. We are developing a new crosslinking approach allowing one to capture the initial stages of nucleosome array self-association and then to analyze its 3D structure using cryo-EM tomography. This experimental approach in combination with 3D chromatin modeling is expected to reveal nanoscale chromatin structural transitions vital for understanding the mechanism(s) of chromatin self-association and liquid-liquid phase separation and for uncovering new types of genetic regulators and pharmacologically active compounds capable of modifying or correcting genetic and epigenetic defects impairing normal cell differentiation and functioning in eukaryotic organisms.