In the crystal structure of cellulose Iβ, disordered hydrogen bonding can be represented by the average of two mutually exclusive hydrogen bonding schemes that have been designated A and B. An unanswered question is whether A and B interconvert dynamically, or whether they are static but present in different regions of the microfibril (giving temporally or a spatially averaged structures, respectively). We have used neutron crystallographic techniques to determine the occupancies of A and B at 295 and 15 K, quantum mechanical calculations to compare the energies of A and B, and molecular dynamics calculations to look at the stability of A. Microfibrils are found to have most chains arranged in a crystalline Iβ structure with hydrogen bonding scheme A. Smaller regions of static disorder exist, perhaps at defects within or between crystalline domains in which the hydrogen bonding is complex but with certain features that are found in B.