Electrically driven light emission from carbon nanotubes(1-8) could be used in nanoscale lasers(9) and single-photon sources(10), and has therefore been the focus of much research. However, high electric fields and currents have either been necessary for electroluminescence(4-8), or have been an undesired side effect(2,3), leading to high power requirements and low efficiencies. Furthermore, electroluminescent linewidths have been broad enough to obscure the contributions of individual optical transitions. Here, we report electrically induced light emission from individual carbon nanotube p-n diodes. A new level of control over electrical carrier injection is achieved, reducing power dissipation by a factor of up to 1,000, and resulting in zero threshold current, negligible self-heating and high carrier-to-photon conversion efficiencies. Moreover, the electroluminescent spectra are significantly narrower (similar to 35 meV) than in previous studies(1-8), allowing the identification of emission from free and localized excitons.