The nearby brown dwarf LP 944 - 20 has been monitored for radial velocity variability at optical and near-infrared wavelengths using the VLT/UVES and the Keck/NIRSPEC spectrographs , respectively . The UVES radial velocity data obtained over 14 nights spanning a baseline of 841 days shows significant variability with an amplitude of 3.5 km s ^ { -1 } . The periodogram analysis of the UVES data indicates a possible period between 2.5 hours and 3.7 hours , which is likely due to the rotation of the brown dwarf . However , the NIRSPEC data obtained over 6 nights shows an rms dispersion of only 0.36 km s ^ { -1 } and do not follow the periodic trend . These results indicate that the variability seen with UVES is likely to be due to rotationally modulated inhomogeneous surface features . We suggest that future planet searches around very low-mass stars and brown dwarfs using radial velocities will be better conducted in the near-infrared than in the optical .