The problem of the origin of biochirality and the related problem of the initial monomer selection are still under discussion, and the main point here is not the mechanics of enantiomer separation but the problem of the role of chirality in the very early stages of evolution. A recent breakthrough in understanding the influence of a static magnetic field on non-magnetic systems can shed light on this complex problem. The phenomenon of magnetosensitivity of non-magnetic systems was reported for only chiral systems and was closely related to the ability of some chiral substances to self-assemble. We suppose the chirality was essential due to the quantum spin-related effects arising between the interacting chiral molecules and providing for the self-assembly phenomenon. Here we demonstrate the magnetosensitivity of the supramolecular packing of cellulose chains, directly indicating the reliability of the supposition above.