Recently, a one-chain monoclinic unit cell for cellulose III(I) having P2(1) symmetry and a single glucose in the asymmetric unit was proposed, based on high-resolution diffraction patterns. The new work challenged a two-chain structure that was published 25 years earlier, although it did not provide new three-dimensional coordinates. Our goals were to solve the structure by modeling, find whether modeling would reject the previously determined two-chain unit cell, and compare the model with the anticipated experimental structure. Combinations of three rotamers of the O-2, O-3, and O-6 hydroxyl groups produced 27 'up' and 27 'down' starting structures. Clusters ('minicrystals') of 13 cellotetraose chains terminated by methyl groups for each of the 54 starting structures were optimized with MM3(96). Hydroxyl groups on 16 of these 54 structures reoriented to give very similar hydrogen-bonding schemes in the interiors, along with the lowest energies. Hydrogen bonds included the usual intramolecular O-3H...O-5' linkage, with O-6' also accepting from O-3H. Interchain hydrogen bonds form an infinite, cooperative O-6H...O-2H...O-6 network. Direct comparison of total minicrystal energies for the one- and two-chain unit cell was inappropriate because the two-chain cell's alternate chains are shifted 0.9 A along the z-axis. To get comparable energy values, models were built with both cellotetraose and cellohexaose chains. The differences in their energies represent the energies for the central layers of cellobiose units. The one-chain cell models had much lower energy. The eight best 'up' one-chain models agree reasonably well with the structure newly determined by experiment.