Dilute aqueous solutions of stiff-chain polyelectrolytes having a poly(p-phenylene) (PPP) backbone were studied by means of electric birefringence and some supplementary conductivity measurements. The PPP polyelectrolytes form molecular solutions, whose electrically induced birefringence rises with field strength according to Kerr's law. From an estimate of the optical anisotropy of the chain backbone, it becomes clear that the anisotropy of the ionic polarizability responsible for the orientation in an electric field is about 5-6 orders of magnitude larger than that of the electronic (optical) polarizability. It increases markedly with rising molecular weight (rod- length) of the polyelectrolyte. The anisotropy of the electric polarizability seems to be due to the ion cloud and not the condensed ions. This interpretation is obtained from a comparison of the changes of electric birefringence and electric conductivity upon addition of a low molecular weight electrolyte.