A problem of substantial interest is to systematically map variation in chromatin structure to gene-expression regulation across conditions, environments, or differentiated cell types. We developed and applied a quantitative framework for determining the existence, strength, and type of relationship between high-resolution chromatin structure in terms of DNaseI hypersensitivity and genome-wide gene-expression levels in 20 diverse human cell types. We show that ∼25% of genes show cell-type-specific expression explained by alterations in chromatin structure. We find that distal regions of chromatin structure (e.g., +/-200 kb) capture more genes with this relationship than local regions (e.g., +/-2.5 kb), yet the local regions show a more pronounced effect. By exploiting variation across cell types, we were capable of pinpointing the most likely hypersensitive sites related to cell-type-specific expression, which we show have a range of contextual uses. This quantitative framework is likely applicable to other settings aimed at relating continuous genomic measurements to gene-expression variation.