We have achieved a record high ratio (19) of the Rabi splitting (3.6 meV) to the polariton linewidth (190 μeV), in a semiconductor λ microcavity with a single 25 nm GaAs quantum well at the antinode. The narrow polariton lines are obtained with a special cavity design which reduces the exciton broadening due to scattering with free charges and has a very low spatial gradient of the cavity resonance energy. Since the static quantum-well disorder is very small, the polariton broadening is dominantly homogeneous. Still, the measured linewidths close to zero detuning cannot be correctly predicted using the linewidth averaging model.