Recently, there has been a growing interest in using induced electro-osmosis to pump fluids in microfluidic devices. We show that induced electro-osmosis can also be used to promote stirring and chaotic advection. To this end, we study theoretically a stirrer in which the flow patterns are alternated in time. We first analyze an idealized embodiment of the stirrer that admits a simple analytical solution for the flow patterns. The stirrer consists of a concentric annulus whose outer surface is defined by an array of electrodes that provide a spatially varying potential distribution. The resulting electric field induces quadruple electro-osmotic flow around the inner cylinder. By timewise alternating the potential distribution around the outer cylinder, we induce chaotic advection in the cavity. Subsequently, we carry out numerical simulations for a more realistic design that can be readily constructed, and demonstrate that it is possible to induce chaotic advection also in this case.