We present a model that predicts the geometry of chromatin fibers as a function of the DNA repeat length. Chromatin fibers are widely observed in vitro and are typically posited as the second level of the hierarchical organization of chromatin in the nuclei of cells. We postulate that the major driving force for fiber formation is the dense packing of the underlying DNAprotein spools, the nucleosomes, allowing for fibers with four possible diameters. We show that the diameters observed in experiments on reconstituted regular fibers correspond to the geometries that minimize the elastic energy of the DNA linking the nucleosomes.