The minimum-energy geometrical structure of the regioregular head-to-tail poly (3-hexylthiophene)(rr-HT-P3HT) polymer has been addressed by means of density functional theory (DFT) calculations which include long-range (van der Waals) interactions. The problem of the P3HT structure has been debated in the literature in the last decades mainly for what concerns the arrangement of the alkyl side chains of the polymer and the type and content of the crystalline primitive cell. The main result of our calculations is that the energetically favored structure of the crystalline polymer at T¼ 0 K corresponds to polythiophene chains with slightly ($168) non co-planar rings and a fishbone arrangement of tilted alkyl side chains with complex internal structure. The alkyl side chains are negligibly interdigitated with those of the adjacent polymer layers; moreover the five terminal carbon atoms of each alkyl side chain are co-planar in all-trans staggered conformation. The optimized geometrical structure obtained for the rr-HT-P3HT polymer is in agreement with measured X-ray spectra of high molecular weight P3HT crystalline samples, and confirms that two non-equivalent polymer chains, mutually shifted along the backbone axis, are contained in an orthorhombic primitive cell.