Few surfaces can exist at rest in either wrinkled or unwrinkled states and switch reversibly between these states. Here, we report a new approach to creating reversibly wrinkling systems using the halogenation of rubber to induce a local increase in the glass-transition temperature within a thin layer at the surface. Such systems are obtained by the bromination of molded rubber films. By means of thermomechanical experiments and in situ observations, we show that microscopic wrinkles are produced by unstretching a stretched film below the glass-transition temperature of the brominated layer. These surface patterns are erased within seconds when the wrinkled layer is heated to above its glass transition and recovers its initial equilibrium dimensions. New wrinkles can be produced and erased repeatedly on the same surface. A model is proposed that takes into account the existence of a gradient in bromine content along the thickness of the modified layer. It describes the viscoelastic behavior of these brominated films and captures the temperature dependencies of the thickness of the glassy layer and of the wrinkle wavelength.