Eukaryotic cells are thought to arrange nucleosomes into extended arrays with evenly spaced nucleosomes phased at genomic landmarks. Here we tested to what extent this stereotypic organization describes the nucleosome organization in Saccharomyces cerevisiae using Fiber-Seq, a long-read sequencing technique that maps entire nucleosome arrays on individual chromatin fibers in a high throughput manner. With each fiber coming from a different cell, Fiber-Seq uncovers cell-to-cell heterogeneity. The long reads reveal the nucleosome architecture even over repetitive DNA such as the ribosomal DNA repeats. The absolute nucleosome occupancy, a parameter that is difficult to obtain with conventional sequencing approaches, is a direct readout of Fiber-Seq. We document substantial deviations from the stereotypical nucleosome organization with unexpectedly long linker DNAs between nucleosomes, gene bodies missing entire nucleosomes, cell-to-cell heterogeneity in nucleosome occupancy, heterogeneous phasing of arrays and irregular nucleosome spacing. Nucleosome array structures are indistinguishable throughout the gene body and with respect to the direction of transcription arguing against transcription promoting array formation. Acute nucleosome depletion destroyed most of the array organization indicating that nucleosome remodelers cannot efficiently pack nucleosomes under those conditions. Given that nucleosomes are cis-regulatory elements, the cell-to-cell heterogeneity uncovered by Fiber-Seq provides much needed information to understand chromatin structure and function.