Mixing by chaotic advection is studied in a new 3-D flow geometry. It consists of two confocal elliptic cylinders whose inner and outer boundaries glide circumferentially so that the geometry does not vary with time. Dye advection experiments have been performed and compared to numerical streak lines calculated using the analytical solution of Stokes'equations in elliptical cylindrical coordinates. Experiments show that particle trajectories remain for all practical purposes inside tubes defined by the potential mixing zone during the whole process. For the case where the elliptic cylinders turn time periodically in opposite directions, we examine the effect of the modulation frequency of the boundary displacement protocol by defining appropriate dimensionless control parameters and then numerically monitoring the advection of a passive scalar. It is shown that for a given average axial velocity, there is an optimum modulation frequency that maximizes the mixing enhancement due to chaotic advection.