Chromatin structure is important in transcription regulation. Many factors influencing chromatin structure have been identified, but the transcriptional programs in which they participate are still poorly understood. Chromatin modifiers participate in transcriptional control together with DNA-bound transcription factors. High-throughput experimental methods allow the genome-wide identification of binding sites for transcription factors as well as quantification of gene expression under various environmental and genetic conditions. We have developed a new methodology that uses the vast amount of available data to dissect the contribution of chromatin structure to transcription. We measure and characterize the dependence of transcription factor function on specific chromatin modifiers. We apply our methodology to S. cerevisiae, using a compendium of 170 gene expression profiles of strains defective for chromatin modifiers, taken from 26 different studies. Our method succeeds in identifying known intricate genetic interactions between chromatin modifiers and transcription factors and uncovers many previously unknown genetic interactions, giving the first genome-wide picture of the contribution of chromatin structure to transcription in a eukaryote.