Translocation of carbohydrate polymers through protein tunnels and clefts is a ubiquitous biochemical phenomenon in proteins such as polysaccharide synthases, glycoside hydrolases, and carbohydrate-binding modules. Although static snapshots of carbohydrate polymer binding in proteins have long been studied via crystallography and spectroscopy, the molecular details of polysaccharide chain processivity have not been elucidated. Here, we employ simulation to examine how a cellulose chain translocates by a disaccharide unit during the processive cycle of a glycoside hydrolase family 7 cellobiohydrolase. Our results demonstrate that these biologically and industrially important enzymes employ a two-step mechanism for chain threading to form a Michaelis complex and that the free energy barrier to chain threading is significantly lower than the hydrolysis barrier. Taken with previous studies, our findings suggest that the rate-limiting step in enzymatic cellulose degradation is the glycosylation reaction, not chain processivity. Based on the simulations, we find that strong electrostatic interactions with polar residues that are conserved in GH7 cellobiohydrolases, but not in GH7 endoglucanases, at the leading glucosyl ring provide the thermodynamic driving force for polysaccharide chain translocation. Also, we consider the role of aromatic carbohydrate interactions, which are widespread in carbohydrate-active enzymes and have long been associated with processivity. Our analysis suggests that the primary role for these aromatic residues is to provide tunnel shape and guide the carbohydrate chain to the active site. More broadly, this work elucidates the role of common protein motifs found in carbohydrate-active enzymes that synthesize or depolymerize polysaccharides by chain translocation mechanisms coupled to catalysis.