The authors report the observation of room-temperature intersubband luminescence at λ=2.13 μm from GaN/AlN quantum wells under optical pumping at λ=0.98 μm. The quantum wells are designed to exhibit three bound states in the conduction band. The emission arises from the e3e2 intersubband transition. Photoluminescence excitation spectroscopy shows that the emission is only observed for p-polarized excitation at wavelengths corresponding to the e1e3 intersubband transition. The measured external quantum efficiency is 10 pW/W.