We show how the optical properties of a single semiconductor quantum dot can be controlled with a small dc voltage applied to a gate electrode. We find that the transmission spectrum of the neutral exciton exhibits two narrow lines with similar to2 mueV linewidth. The splitting into two linearly polarized components arises through an exchange interaction within the exciton. The exchange interaction can be turned off by choosing a gate voltage where the dot is occupied with an additional electron. Saturation spectroscopy demonstrates that the neutral exciton behaves as a two-level system. Our experiments show that the remaining problem for manipulating excitonic quantum states in this system is spectral fluctuation on a mueV energy scale.