Polarized infrared optical emission was observed from a carbon nanotube ambipolar field-effect transistor (FET). An effective forward-biased p-n junction, without chemical dopants, was created in the nanotube by appropriately biasing the nanotube device. Electrical measurements show that the observed optical emission originates from radiative recombination of electrons and holes that are simultaneously injected into the undoped nanotube. These observations are consistent with a nanotube FET model in which thin Schottky barriers form at the source and drain contacts. This arrangement is a novel optical recombination radiation source in which the electrons and holes are injected into a nearly field-free region. Such a source may form the basis for ultrasmall integrated photonic devices.