DNA accessibility is thought to be of major importance in regulating gene expression. We test this hypothesis using a restriction enzyme as a probe of chromatin structure and as a proxy for transcription factors. We measured the digestion rate and the fraction of accessible DNA at almost all genomic AluI sites in budding yeast and mouse liver nuclei. Hepatocyte DNA is more accessible than yeast DNA, consistent with longer linkers between nucleosomes, suggesting that nucleosome spacing is a major determinant of accessibility. DNA accessibility varies from cell to cell, such that essentially no sites are accessible or inaccessible in every cell. AluI sites in inactive mouse promoters are accessible in some cells, implying that transcription factors could bind without activating the gene. Euchromatin and heterochromatin have very similar accessibilities, suggesting that transcription factors can penetrate heterochromatin. Thus, DNA accessibility is not likely to be the primary determinant of gene regulation.