We report transport of electron-hole complexes in semiconductor quantum wells under applied electric fields. Negatively charged excitons (X-), created by laser excitation of a high electron mobility transistor, are observed to drift upon applying a voltage between the source and drain. In contrast, neutral excitons do not drift under similar conditions. The X- mobility is found to be as high as 6.5 x 10(4) cm2 V-1 s-1. The results demonstrate that X- exists as a free particle in the best-quality samples and suggest that light emission from opto-electronic devices can be manipulated through exciton drift under applied electric fields.