Small-angle neutron scattering (SANS) data for solutions containing a highly charged cationic polyelectrolyte and an anionic surfactant are presented. The scattering data were obtained in pure D2O, emphasizing the scattering from the polyelectrolyte, and in a H2O/D2O mixture that contrast matches the polyelectrolyte. In the absence of surfactant, a broad scattering peak due to the mesh size of the polyelectrolyte solution is the most characteristic feature. This peak moves to larger q-values (smaller distances) as the polyelectrolyte concentration is increased, as expected for a semidilute polyelectrolyte solution. Addition of a small amount of surfactant reduces and finally removes this peak. Instead a sharp diffraction peak appears at high q-values. This Bragg peak corresponds to a characteristic distance of 37-39 Å, and it is observed when either the polyelectrolyte or the surfactant is contrast matched by the solvent. Once this peak has appeared, its position does not change when the surfactant concentration is increased. The intensity of the peak grows, however, until a stoichiometric polyelectrolyte-surfactant complex has been formed. The Bragg peak remains in excess surfactant solution. These results are discussed in relation to the structure of the polyelectrolyte-surfactant aggregates and in connection with recent results from surface force and turbidity measurements using the same polyelectrolyte-surfactant pair.