DNA wrapped in nucleosomes is sterically occluded, creating obstacles for polymerase, regulatory, remodeling, repair and recombination complexes, which require access to the wrapped DNA. How such complexes recognize and gain access to their DNA target sites is not known. Here we report the direct detection of a dynamic equilibrium conformational transition in nucleosomes that greatly increases the distance between the end of the nucleosomal DNA and the histone core. We quantified the equilibrium constant for this transition under physiological conditions. As predicted by these findings, addition of LexA protein to nucleosomes containing the LexA target site drives this conformational equilibrium toward the unwrapped, accessible state, simultaneously allowing stable LexA binding. This inherent property of nucleosomes allows any protein, whether an energy-dependent machine or a passive binder, to gain access even to buried stretches of nucleosomal DNA.