The radial velocities of low mass stars and brown dwarfs will be studied using a combination of interferometry and multichannel dispersive spectroscopy, called Externally Dispersed Interferometry. This technique will allow enhancements of spectral and Doppler velocity resolution of existing echelle or linear grating spectrographs. Externally Dispersed Interferometry has the potential to greatly improve the performance of spectroscopy at a broad range of astronomical facilities.