We report measurements of a coherent coupling between surface plasmon polaritons (SPP) and quantum well excitons in a hybrid metal-semiconductor nanostructure. The hybrid structure is designed to optimize the radiative exciton-SPP interaction which is probed by low-temperature, angle-resolved, far-field reflectivity spectroscopy. As a result of the coupling, a significant shift of approximately 7 meV and an increase in broadening by approximately 4 meV of the quantum well exciton resonance are observed. The experiments are corroborated by a phenomenological coupled-oscillator model predicting coupling strengths as large as 50 meV in structures with optimized detunings between the coupled exciton and SPP resonances. Such a strong interaction can, e.g., be used to enhance the luminescence yield of semiconductor quantum structures or to amplify SPP waves.