DNase I‐hypersensitive sites lack a canonical nucleosome and have binding sites for various transcription factors. To understand how the hypersensitivity is generated and maintained, we studied the chicken erythroid‐specific beta(A)/epsilon globin gene enhancer, a region where both tissue‐specific and ubiquitous transcription factors can bind. Constructions containing mutations of this enhancer were stably introduced into a chicken erythroid cell line. We found that the hypersensitivity was determined primarily by the erythroid factors and that their binding additively increased the accessibility. The fraction of accessible sites in clonal cell lines was quantitated using restriction endonucleases; these data implied that the formation of each hypersensitive site was an all‐or‐none phenomenon. Use of DNase I and micrococcal nuclease probes further indicated that the size of the hypersensitive site was influenced by the binding of transcription factors which then determined the length of the nucleosome‐free gap. Our data are consistent with a model in which hypersensitive sites are generated stochastically: mutations that reduce the number of bound factors reduce the probability that these factors will prevail over a nucleosome; thus, the fraction of sites in the population that are accessible is also diminished.