We report on the strong coupling between inorganic quantum well excitons and surface plasmons. For that purpose a corrugated silver film was deposited on the top of a heterostructure consisting of GaAs/GaAlAs quantum wells. The formation of plasmon/heavy-hole exciton/light-hole exciton mixed states is demonstrated with reflectometry experiments. The interaction energies amount to 21 meV for the plasmon/light-hole exciton and 22 meV for the plasmon/heavy-hole exciton. Some particularities of the plasmon-exciton coupling were also discussed and qualitatively related to the plasmon polarization.