Highly charged intrinsically disordered proteins are essential regulators of chromatin structure and transcriptional activity. Here we identify a surprising mechanism of molecular competition that relies on the pronounced dynamical disorder present in these polyelectrolytes and their complexes. The highly positively charged human linker histone H1.0 (H1) binds to nucleosomes with ultrahigh affinity, implying residence times incompatible with efficient biological regulation. However, we show that the disordered regions of H1 retain their large-amplitude dynamics when bound to the nucleosome, which enables the highly negatively charged and disordered histone chaperone prothymosin alpha to efficiently invade the H1-nucleosome complex and displace H1 via a competitive substitution mechanism, vastly accelerating H1 dissociation. By integrating experiments and simulations, we establish a molecular model that rationalizes the remarkable kinetics of this process structurally and dynamically. Given the abundance of polyelectrolyte sequences in the nuclear proteome, this mechanism is likely to be widespread in cellular regulation.