The rheological properties of aqueous solutions of poly(acrylic acid) and an oppositely charged surfactant, dodecyltrimethylammonium bromide (C(12)TAB), are reported. The solution viscosity decreases rapidly as surfactant is added. The effects of polymer molecular weight, polymer concentration, and polymer charge have been studied with no added salt. The results are compared with the predictions of a simple model based on the scaling theory for the viscosity of unentangled semidilute polyelectrolyte solutions in good solvent.(1) This model takes into account two effects of added surfactant. The effective chain length of the polyelectrolyte is shortened when a significant fraction of the length wraps around micelles, and an effective addition of salt arises from the polyelectrolyte and surfactant counterions, further lowering the viscosity. The only parameter used in this model is independently determined using an ion-selective electrode, allowing the model to make a quantitative prediction of solution viscosity for strongly charged polyelectrolytes with no adjustable parameters. Comparison with literature data for weakly charged polyelectrolytes suggests only partial binding of polymer to the micelle surface in this case.