Electroconvection in a thin, sheared fluid film displays a rich sequence of bifurcations between different flow states as the driving voltage is increased. We present a numerical study of an annular film in which a radial potential difference acts on induced surface charges to drive convection. The film is also sheared by independently rotating the inner edge of the annulus. This simulation models laboratory experiments on electroconvection in sheared smectic liquid crystal films. The applied shear competes with the electrical forces, resulting in oscillatory and strongly subcritical bifurcations between localized vortex states close to onset. At higher forcing, the flow becomes chaotic via a Ruelle-Takens-Newhouse scenario. The simulation allows flow visualization not available in the physical experiments, and sheds light on previously observed transitions in the current-voltage characteristics of electroconvecting smectic films.