The addition of positively charged, 30 nm diameter silica nanoparticles to cationic wormlike micellar solutions of cetyltrimethylammonium bromide and sodium nitrate is studied using a combination of rheology, small angle neutron scattering, dynamic light scattering, and cryo-transmission electron microscopy. The mixtures are single phase up to particle volume fractions of 1%. The addition of like-charged particles significantly increases the wormlike micelle (WLM) solution's zero shear rate viscosity, longest relaxation time, and storage modulus. The changes are hypothesized to originate from a close association of the particles with the micellar mesh. Small angle neutron scattering measurements with contrast matching demonstrate associations between particles mitigated by the WLMs. The effective interparticle interactions measured by SANS can explain the observed phase behavior. Dynamic light scattering measurements confirm the dynamic coupling of the particles to the micellar mesh.