Nucleosomes are regularly spaced along eukaryotic genomes. In the emerging model, known as "statistical positioning", this spacing is due to steric repulsion between nucleosomes and to the presence of nucleosome excluding barriers on the genome. However, new experimental evidence recently challenged the "statistical positioning" model (Z. Zhang et al., Science, 2011, 332(6032), 977-980). We propose here that the regular spacing can be better explained by adding attractive interactions between nucleosomes. In our model those attractions are due to the fact that nucleosomes are stacked in regular chromatin fibers. In a self-reinforcing mechanism, regular nucleosome spacing promotes in turn nucleosome stacking. We first show that this model can precisely account for the nucleosome spacing observed in Saccharomyces cerevisiae. We then use a simple toy model to show that attraction between nucleosomes can fasten the formation of the chromatin fiber.