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We developed a chemical cleavage method that releases single nucleosome dyad-containing fragments, allowing us to precisely map both single nucleosomes and linkers with high accuracy genome-wide in yeast. Our single nucleosome positioning data reveal that nucleosomes occupy preferred positions that differ by integral multiples of the DNA helical repeat. By comparing nucleosome dyad positioning maps to existing genomic and transcriptomic data, we evaluated the contributions of sequence, transcription, and histones H1 and H2A.Z in defining the chromatin landscape. We present a biophysical model that neglects DNA sequence and shows that steric occlusion suffices to explain the salient features of nucleosome positioning.