The remarkable mechanical strength of cellulose reflects the arrangement of multiple β-1,4-linked glucan chains in a para-crystalline fibril. During plant cellulose biosynthesis, a multimeric cellulose synthesis complex (CSC) moves within the plane of the plasma membrane as many glucan chains are synthesized from the same end and in close proximity. Many questions remain about the mechanism of cellulose fibril assembly, for example must multiple catalytic subunits within one CSC polymerize cellulose at the same rate? How does the cellulose fibril bend to align horizontally with the cell wall? Here we used mathematical modeling to investigate the interactions between glucan chains immediately after extrusion on the plasma membrane surface. Molecular dynamics simulations on groups of six glucans, each originating from a position approximating its extrusion site, revealed initial formation of an uncrystallized aggregate of chains from which a protofibril arose spontaneously through a ratchet mechanism involving hydrogen bonds and van der Waals interactions between glucose monomers. Consistent with the predictions from the model, freeze-fracture transmission electron microscopy using improved methods revealed a hemispherical accumulation of material at points of origination of apparent cellulose fibrils on the external surface of the plasma membrane where rosette-type CSCs were also observed. Together the data support the possibility that a zone of uncrystallized chains on the plasma membrane surface buffers the predicted variable rates of cellulose polymerization from multiple catalytic subunits within the CSC and acts as a flexible hinge allowing the horizontal alignment of the crystalline cellulose fibrils relative to the cell wall.