The exact positions of nucleosomes along genomic DNA can influence many aspects of chromosome function. However, existing methods for mapping nucleosomes do not provide the necessary single-base-pair accuracy to determine these positions. Here we develop and apply a new approach for direct mapping of nucleosome centres on the basis of chemical modification of engineered histones. The resulting map locates nucleosome positions genome-wide in unprecedented detail and accuracy. It shows new aspects of the in vivo nucleosome organization that are linked to transcription factor binding, RNA polymerase pausing and the higher-order structure of the chromatin fibre.