Stable Au nanoshell-J-aggregate complexes are formed that exhibit coherent coupling between the localized plasmons of a nanoshell and the excitons of molecular J-aggregates adsorbed on its surface. By tuning the nanoshell plasmon energies across the exciton line of the J-aggregate, plasmon-exciton coupling energies for these complexes are obtained. The strength of this interaction is dependent on the specific plasmon mode of the nanoparticle coupled to the J-aggregate exciton. From a model based on Gans theory, we obtain an expression for the plasmon-exciton hybridized states of the complex.