Cellobiohydrolases processively hydrolyze glycosidic linkages in individual polymer chains of cellulose microfibrils, and typically exhibit specificity for either the reducing or nonreducing end of cellulose. Here, we conduct molecular dynamics simulations and free energy calculations to examine the initial binding of a cellulose chain into the catalytic tunnel of the reducing-end-specific Family 7 cellobiohydrolase (Cel7A) from Hypocrea jecorina. In unrestrained simulations, the cellulose diffuses into the tunnel from the -7 to the -5 positions, and the associated free energy profiles exhibit no barriers for initial processivity. The comparison of the free energy profiles for different cellulose chain orientations show a thermodynamic preference for the reducing end, suggesting that the preferential initial binding may affect the directional specificity of the enzyme by impeding nonproductive (nonreducing end) binding. Finally, the Trp-40 at the tunnel entrance is shown with free energy calculations to have a significant effect on initial chain complexation in Cel7A.