Ordered nanostructures of cuprous oxide are deposited onto single-crystal gold after a transition from a thermodynamically controlled orientation to a kinetically preferred orientation. Crosshatch patterns of cuprous oxide with a 20 by 100 nm orthogonal nanowire morphology are formed at pH 12 on Au(100). A unique asset of electrodeposition is exploited to deposit these nanostructures: the departure from equilibrium is controlled with millivolt precision by simply selecting an applied electrode overpotential. Small changes in overpotential produce dramatic changes in the morphology of the films. The electrodeposited films follow the [100] orientation of the single-crystal substrate at low overpotential (that is, close to equilibrium) but change to a kinetically preferred [ 110] orientation at a threshold overpotential of -118 mV. The abrupt change of orientation is triggered by the coalescence of three-dimensional islands that form on the Au(100) surface.