Using first-principles methods and 8-band k·p simulations, we study the electronic structure of an ultrathin quantum-well system consisting of a single layer of InN inserted in GaN matrix. Experimental photoluminescence and electroluminescence emission peaks for such structures have been reported in the wavelength region between 380 to 450 nm. In contrast, our calculations show an energy difference between the electron and hole states around 2.17 eV (573 nm). Possible origins of the experimental light emission are examined. We suggest that the experimental emission may be due to recombination of electrons (holes) in GaN with holes (electrons) in the quantum well.