Genomic DNA is packaged into chromatin in eukaryotic cells. The fundamental building block of chromatin is the nucleosome, a 147 bp-long DNA segment wrapped around the surface of a histone octamer. Nucleosomes function to compact genomic DNA and to regulate access to it both by physical occlusion and by providing the substrate for numerous covalent epigenetic tags. We have studied intrinsic sequence specificity of histone-DNA interactions by using a high-throughput map of nucleosomes assembled in vitro on yeast and E.coli genomic DNA. We have inferred free energies of nucleosome formation genome-wide using a biophysical model that rigorously takes steric exclusion between neighboring nucleosomes into account. Surprisingly, most S.cerevisiae nucleosomes do not appear to be positioned by periodic dinucleotide patterns or by exclusion of longer sequence motifs such as poly(dA:dT) tracts - rather, their locations are simply controlled by the dinucleotide content of the underlying DNA sequence. Similar nucleosome positioning rules emerge from the studies of C.elegans chromatin and even from nucleosome-free control experiments, likely because histone sequence preferences are correlated with those revealed by sonicating nucleosome-free genomic DNA or digesting it with MNase. Our findings suggest that the nature of the nucleosome positioning code is fairly simple. Nucleosome energetics based on dinucleotide biases would make it easier to evolve and maintain nucleosome positioning sequences in eukaryotic genomes. Such sequences could then be refined and strengthened with 10-11 bp periodic dinucleotide patterns.