We present the results of an infrared spectroscopic survey of 23 late-M dwarfs with the NIRSPEC echelle spectrometer on the Keck II telescope. Using telluric lines for wavelength calibration, we are able to achieve measurement precisions of down to 45 m s{sup -1} for our late-M dwarfs over a one- to four-year long baseline. Our sample contains two stars with radial velocity (RV) variations of >1000 m s{sup -1}. While we require more measurements to determine whether these RV variations are due to unseen planetary or stellar companions or are the result of starspots known to plague the surface of M dwarfs, we can place upper limits of <40 M{sub J} sin i on the masses of any companions around those two M dwarfs with RV variations of <160 m s{sup -1} at orbital periods of 10-100 days. We have also measured the rotational velocities for all the stars in our late-M dwarf sample and offer our multi-order, high-resolution spectra over 2.0-2.4 {mu}m to the atmospheric modeling community to better understand the atmospheres of late-M dwarfs.