Semiconducting carbon nanotubes promise a broad range of potential applications in optoelectronics and imaging, but their photon-conversion efficiency is relatively low. Quantum theory suggests that nanotube photoluminescence is intrinsically inefficient because of low-lying 'dark' exciton states. Here we demonstrate the significant brightening of nanotube photoluminescence (up to 28-fold) through the creation of an optically allowed defect state that resides below the predicted energy level of the dark excitons. Emission from this new state generates a photoluminescence peak that is red-shifted by as much as 254 meV from the nanotube's original excitonic transition. We also found that the attachment of electron-withdrawing substituents to carbon nanotubes systematically drives this defect state further down the energy ladder. Our experiments show that the material's photoluminescence quantum yield increases exponentially as a function of the shifted emission energy. This work lays the foundation for chemical control of defect quantum states in low-dimensional carbon materials.