Genome-wide chromatin state underlies gene expression potential and cellular function. Epigenetic features and nucleosome positioning contribute to the accessibility of DNA, but widespread regulators of chromatin state are largely unknown. Our study investigates how coordination of ANP32E and H2A.Z contributes to genome-wide chromatin state in mouse fibroblasts. We define H2A.Z as a universal chromatin accessibility factor, and demonstrate that ANP32E antagonizes H2A.Z accumulation to restrict chromatin accessibility genome-wide. In the absence of ANP32E, H2A.Z accumulates at promoters in a hierarchical manner. H2A.Z initially localizes downstream of the transcription start site, and if H2A.Z is already present downstream, additional H2A.Z accumulates upstream. This hierarchical H2A.Z accumulation coincides with improved nucleosome positioning, heightened transcription factor binding, and increased expression of neighboring genes. Thus, ANP32E dramatically influences genome-wide chromatin accessibility through subtle refinement of H2A.Z patterns, providing a means to reprogram chromatin state and to hone gene expression levels.