Chromatin structure undergoes many changes during the cell cycle and in response to regulatory events. A basic unit of chromatin organization is the nucleosome core particle. However, very little is known about how nucleosomes are arranged into higher-order structures in vivo, even though the efficiency and precision of cell division imply high levels of structural organization. We propose abandoning the current paradigm of chromatin organization based on thermodynamics of the lowest energy state and replace it with the idea of a topologically restrained, high-energy structure. We propose that DNA is subject to a recursive topological restraint, and is anchored by hemicatenates that are part of the chromosomal scaffold. Long-distance _cis_-regulation of transcription is a natural consequence of recursive topological restraint. This new theory of chromatin structure has a multitude of consequences for key aspects of cellular biology