Regular successions of positioned nucleosomes, or phased nucleosome arrays (PNAs), are predominantly known from transcriptional start sites (TSSs). It is unclear whether PNAs occur elsewhere in the genome. To generate a comprehensive inventory of PNAs for Drosophila, we applied spectral analysis to nucleosome maps and identified thousands of PNAs throughout the genome. About half of them are not near TSSs and are strongly enriched for an uncharacterized sequence motif. Through genome-wide reconstitution of physiological chromatin in Drosophila embryo extracts, we uncovered the molecular basis of PNA formation. We identified Phaser, an unstudied zinc finger protein that positions nucleosomes flanking the motif. It also revealed how the global activity of the chromatin remodelers CHRAC/ACF, together with local barrier elements, generates islands of regular phasing throughout the genome. Our work demonstrates the potential of chromatin assembly by embryo extracts as a powerful tool to reconstitute chromatin features on a global scale in vitro.