In Drosophila embryos, many biochemically and functionally unrelated transcription factors bind quantitatively to highly overlapping sets of genomic regions, with much of the lowest levels of binding being incidental, non-functional interactions on DNA. The primary biochemical mechanisms that drive these genome-wide occupancy patterns have yet to be established.Here we use data resulting from the DNaseI digestion of isolated embryo nuclei to provide a biophysical measure of the degree to which proteins can access different regions of the genome. We show that the in vivo binding patterns of 21 developmental regulators are quantitatively correlated with DNA accessibility in chromatin. Furthermore, we find that levels of factor occupancy in vivo correlate much more with the degree of chromatin accessibility than with occupancy predicted from in vitro affinity measurements using purified protein and naked DNA. Within accessible regions, however, the intrinsic affinity of the factor for DNA does play a role in determining net occupancy, with even weak affinity recognition sites contributing. Finally, we show that programmed changes in chromatin accessibility between different developmental stages correlate with quantitative alterations in factor binding.Based on these and other results, we propose a general mechanism to explain the widespread, overlapping DNA binding by animal transcription factors. In this view, transcription factors are expressed at sufficiently high concentrations in cells such that they can occupy their recognition sequences in highly accessible chromatin without the aid of physical cooperative interactions with other proteins, leading to highly overlapping, graded binding of unrelated factors.