A multiscale simulation model is used to construct potential and free energy surfaces for the carbohydrate-binding module [CBM] from an industrially important cellulase, Trichoderma reesei cellobiohydrolase 1, on the hydrophobic face of a coarse-grained cellulose 1 beta polymorph. We predict from computation that the CBM alone exhibits regions of stability on the hydrophobic face of cellulose every 5 and 10 angstrom, corresponding to a glucose unit and a cellobiose unit, respectively. In addition, we predict a new role for the CBM: specifically, that in the presence of hydrolyzed cellulose chain ends, the CBM exerts a thermodynamic driving force to translate away from the free cellulose chain ends. This suggests that the CBM is not only required for binding to cellulose, as has been known for two decades, but also that it has evolved to both assist the enzyme in recognizing a cellulose chain end and exert a driving force on the enzyme during processive hydrolysis of cellulose.