Nucleosomes are important for gene regulation because their arrangement on the genome can control which proteins bind to DNA. Currently, few human nucleosomes are thought to be consistently positioned across cells; however, this has been difficult to assess due to the limited resolution of existing data. We performed paired-end sequencing of micrococcal nuclease-digested chromatin (MNase-seq) from seven lymphoblastoid cell lines and mapped over 3.6 billion MNase-seq fragments to the human genome to create the highest-resolution map of nucleosome occupancy to date in a human cell type. In contrast to previous results, we find that most nucleosomes have more consistent positioning than expected by chance and a substantial fraction (8.7%) of nucleosomes have moderate to strong positioning. In aggregate, nucleosome sequences have 10 bp periodic patterns in dinucleotide frequency and DNase I sensitivity; and, across cells, nucleosomes frequently have translational offsets that are multiples of 10 bp. We estimate that almost half of the genome contains regularly spaced arrays of nucleosomes, which are enriched in active chromatin domains. Single nucleotide polymorphisms that reduce DNase I sensitivity can disrupt the phasing of nucleosome arrays, which indicates that they often result from positioning against a barrier formed by other proteins. However, nucleosome arrays can also be created by DNA sequence alone. The most striking example is an array of over 400 nucleosomes on chromosome 12 that is created by tandem repetition of sequences with strong positioning properties. In summary, a large fraction of nucleosomes are consistently positioned--in some regions because they adopt favored sequence positions, and in other regions because they are forced into specific arrangements by chromatin remodeling or DNA binding proteins.