Cooperative binding of transcription factors (TFs) to promoters and other regulatory regions is essential for precise gene expression. The classical model of cooperativity requires direct interactions between TFs, thus constraining the arrangement of TF sites in regulatory regions. Recent genomic and functional studies, however, demonstrate a great deal of flexibility in such arrangements with variable distances, numbers of sites, and identities of TF sites located in cis-regulatory regions. Such flexibility is inconsistent with cooperativity by direct interactions between TFs. Here, we demonstrate that strong cooperativity among noninteracting TFs can be achieved by their competition with nucleosomes. We find that the mechanism of nucleosome-mediated cooperativity is analogous to cooperativity in another multimolecular complex: hemoglobin. This surprising analogy provides deep insights, with parallels between the heterotropic regulation of hemoglobin (e.g., the Bohr effect) and the roles of nucleosome-positioning sequences and chromatin modifications in gene expression. Nucleosome-mediated cooperativity is consistent with several experimental studies, is equally applicable to repressors and activators, allows substantial flexibility in and modularity of regulatory regions, and provides a rationale for a broad range of genomic and evolutionary observations. Striking parallels between cooperativity in hemoglobin and in transcriptional regulation point to a general mechanism that can be used in various biological systems.