Room-temperature polariton lasing from a GaN-dielectric microcavity is demonstrated with optical excitation. The device is fabricated with a GaN nanowire array clad by Si3N4/SiO2-distributed Bragg reflectors. The nanowire array is initially grown on silicon substrate by molecular beam epitaxy. A distinct nonlinearity in the lower polariton emission is observed at a threshold optical energy density of 625 nJ/cm(2), accompanied by significant line width narrowing to 5 meV and a small blue shift of ~1 meV. The measured polariton dispersion is characterized by a Rabi splitting of 40 meV and a cavity exciton detuning of -17 meV. The device described here is a demonstration of exciton-photon strong coupling phenomenon in an array of light emitters and paves the way for the realization of a room temperature electrically injected polariton laser.