We report on strong coupling between surface plasmon polaritons on a thin silver film and laser dye Rhodamine 800. Attenuated total reflection measurements reveal that the pure surface plasmon polaritons interact with the Rhodamine 800 absorption lines exhibiting pronounced anticrossings in the dispersion relation. We show that the corresponding energy gap can be tailored by the concentration of dye molecules in the dielectric matrix between 50 meV and 70 meV. We can well model our data by a classical transfer matrix approach as well as by a quantum mechanical coupled oscillator ansatz.