SignificanceClassically, the lifetime of a protein–ligand complex is presumed to be an intrinsic property, unaffected by competitor molecules in free solution. By contrast, a few oligomeric nucleic acid–binding proteins have been observed to exchange competing ligands in their binding sites, and consequently their lifetimes decrease with competitor concentration. Our findings suggest that this “direct transfer” capability may be a more general property of nucleic acid– binding proteins. Thus, many DNA- and RNA-binding proteins could reduce the dimensionality of their search for their target sites by direct transfer to nucleosome DNA, instead of relying entirely on three-dimensional diffusion. Furthermore, direct transfer from nascent RNA to DNA may explain why so many DNA-binding proteins also bind RNA.