Cellobiohydrolases (CBHs) make up an important group of enzymes for both natural carbon cycling and industrial deconstruction of lignocellulosic biomass. The consecutive hydrolysis of one cellulose strand relies on an intricate pattern of enzyme–substrate interactions in the long, tunnel-shaped binding site of the CBH. In this work, we have investigated the initial complexation mode with cellulose of the most thoroughly studied CBH, Cel7A from Hypocrea jecorina (HjCel7A). We found that HjCel7A predominantly produces glucose when it initiates a processive run on insoluble microcrystalline cellulose, confirming the validity of an even and odd product ratio as an estimate of processivity. Moreover, the glucose released from cellulose was predominantly α-glucose. A link between the initial binding mode of the enzyme and the reducing end configuration was investigated by inhibition studies with the two anomers of cellobiose. A clear preference for β-cellobiose in product binding site +2 was observed for HjCel7A, but not the homologous endoglucanase, HjCe7B. Possible relationships between this anomeric preference in the product site and the prevalence of odd-numbered initial-cut products are discussed, and a correlation between processivity and anomer selectivity is proposed.