The compaction of eukaryotic DNA into chromatin has been implicated in the regulation of all DNA processes. To unravel the higher-order folding of chromatin, we used magnetic tweezers and probed the mechanical properties of single 197-bp repeat length arrays of 25 nucleosomes. At forces up to 4 pN, the 30-nm fiber stretches like a Hookian spring, resulting in a three-fold extension. Together with a high nucleosome-nucleosome stacking energy, this points to a solenoid as the underlying topology of the 30-nm fiber. Unexpectedly, linker histones do not affect the length or stiffness of the fiber but stabilize its folding. Fibers with a nucleosome repeat length of 167 bp are stiffer, consistent with a two-start helical arrangement. The observed high compliance causes extensive thermal breathing, which forms a physical basis for the balance between DNA condensation and accessibility.