The authors report on the demonstration of strong light-matter coupling at room temperature using a crack-free UV microcavity containing GaN/AlGaN quantum wells (QWs). Lattice-matched AlInN/AlGaN distributed Bragg reflectors (DBRs) with a maximum peak reflectivity of 99.5% and SiO2/Si 3N4 DBRs were used to form high finesse hybrid microcavities. State-of-the-art GaN/Al0.2Ga0.8N QWs emitting at 3.62 eV with a linewidth of 45 meV at 300 K were inserted in these structures. For a 3λ/2 microcavity containing six QWs, the interaction between cavity photons and QW excitons is sufficiently large to reach the strong coupling regime. A polariton luminescence is observed with a vacuum field Rabi splitting of 30 meV at 300 K.