Many glycoside hydrolase (GH) enzymes act via a processive mechanism whereby an individual carbohydrate polymer chain is decrystallized and hydrolyzed along the chain without substrate dissociation. Despite considerable structural and biochemical studies, a molecular-level theory of processivity that relates directly to structural features of GH enzymes does not exist. Here, we hypothesize that the degree of processivity is directly linked to the ability of an enzyme to decrystallize a polymer chain from a crystal, quantified by the binding free energy of the enzyme to the cello-oligosaccharide. We develop a simple mathematical relationship formalizing this hypothesis to quantitatively relate the binding free energy to experimentally measurable kinetic parameters. We then calculate the absolute ligand binding free energy of cellulose chains to the biologically and industrially important GH Family 7 processive cellulases with free energy perturbation/replica-exchange molecular dynamics. Taken with previous observations, our results suggest that degree of processivity is directly correlated to the binding free energy of cello-oligosaccharide ligands to GH7s. The observed binding free energies also suggest candidate polymer morphologies susceptible to enzyme action when compared to the work required to decrystallize cellulose chains. We posit that the ligand binding free energy is a key parameter in comparing the activity and function of GHs and may offer a molecular-level basis toward a general theory of carbohydrate processivity in GHs and other enzymes able to process linear carbohydrate polymers, such as cellulose and chitin synthases.