Precise gene expression patterns are established by transcription factor (TFs) binding to regulatory sequences. While these events occur in the context of chromatin, our understanding of how TF-nucleosome interplay affects gene expression is highly limited. Here, we present an assay for high-resolution measurements of both DNA occupancy and gene expression on large-scale libraries of systematically designed regulatory sequences. Our assay reveals occupancy patterns at the single-cell level. It provides an accurate quantification of the fraction of the population bound by a nucleosome and captures distinct, even adjacent, TF binding events. By applying this assay to over 1,500 promoter variants in yeast, we reveal pronounced differences in the dependency of TF activity on chromatin and classify TFs by their differential capacity to alter chromatin and promote expression. We further demonstrate how different regulatory sequences give rise to nucleosome-mediated TF collaborations that quantitatively account for the resulting expression.