Cation exchange reactions modify the composition of a nanocrystal while retaining other features, including the crystal structure and morphology. In many cases, the anion sublattice is considered to be locked in place as cations rapidly shuttle in and out. Here we provide evidence that the anion sublattice can shift significantly during nanocrystal cation exchange reactions. When the Cu+ cations of roxbyite Cu1.8S nanorods exchange with Zn2+ to form ZnS nanorods, a high density of stacking faults emerges. During cation exchange, the stacking sequence of the close-packed anion sublattice shifts at many locations to generate a nanorod product containing a mixture of wurtzite, zincblende, and a wurtzite/zincblende polytype that contains an ordered arrangement of stacking faults. The reagent concentration and reaction temperature, which control the cation exchange rate, serve as synthetic levers that can tune the stacking fault density from high to low, which is important because once introduced, the stacking faults could not be modified through thermal annealing. This level of synthetic control through nanocrystal cation exchange is important for controlling properties that depend on the presence and density of stacking faults.