In this Letter, we demonstrate a reversible strong coupling regime between a dipolar surface plasmon resonance and a molecular excited state. This reversible state is experimentally observed on silver nanoparticle arrays embedded in a polymer film containing photochromic molecules. Extinction measurements reveal a clear Rabi splitting of 294 meV, corresponding to ~13% of the molecular transition energy. We derived an analytical model to confirm our observations, and we emphasize the importance of spectrally matching the polymer absorption with the plasmonic resonance to observe coupled states. Finally, the reversibility of this coupling is illustrated by cycling the photochromic molecules between their two isomeric forms.