Most nucleosomes are well-organized at the 5' ends of S. cerevisiae genes where "-1" and "+1" nucleosomes bracket a nucleosome-free promoter region (NFR). How nucleosomal organization is specified by the genome is less clear. Here we establish and inter-relate rules governing genomic nucleosome organization by sequencing DNA from more than one million immunopurified S. cerevisiae nucleosomes (displayed at http://atlas.bx.psu.edu/). Evidence is presented that the organization of nucleosomes throughout genes is largely a consequence of statistical packing principles. The genomic sequence specifies the location of the -1 and +1 nucleosomes. The +1 nucleosome forms a barrier against which nucleosomes are packed, resulting in uniform positioning, which decays at farther distances from the barrier. We present evidence for a novel 3' NFR that is present at >95% of all genes. 3' NFRs may be important for transcription termination and anti-sense initiation. We present a high-resolution genome-wide map of TFIIB locations that implicates 3' NFRs in gene looping.