Magnetic tweezers were used to study the mechanical response under torsion of single nucleosome arrays reconstituted on tandem repeats of 5S positioning sequences. Regular arrays are extremely resilient and can reversibly accommodate a large amount of supercoiling without much change in length. This behavior is quantitatively described by a molecular model of the chromatin three-dimensional architecture. In this model, we assume the existence of a dynamic equilibrium between three conformations of the nucleosome, corresponding to different crossing statuses of the entry/exit DNAs (positive, null or negative, respectively). Torsional strain displaces that equilibrium, leading to an extensive reorganization of the fiber's architecture. The model explains a number of long-standing topological questions regarding DNA in chromatin and may provide the basis to better understand the dynamic binding of chromatin-associated proteins.Note: In the supplementary information initially published online to accompany this article, Supplementary Figure 2 was mistakenly replaced by Supplementary Equation 2. The error has been corrected online.