We present evidence for a mechanism by which regulatory proteins may gain access to their target DNA sequences in chromatin. In this model, nucleosomes are dynamic structures, transiently exposing stretches of their DNA. Regulatory proteins gain access to DNA target sites in the exposed state, and bind with an apparent dissociation constant equal to their dissociation constant for naked DNA divided by a position-dependent equilibrium constant for site exposure within the nucleosome. A sensitive assay, based on the kinetics of restriction digestion of sites within nucleosomes, reveals this dynamic behaviour and quantifies the equilibrium constants for site exposure. Our results have implications for many aspects of chromatin function. They offer new mechanisms for cooperativity (synergy) in regulatory protein binding and for active invasion of nucleosomes.