We present a precise kinematic study of very young brown dwarfs in the Cha I cloud based on radial velocities ( RVs ) measured with UVES at the VLT . The kinematics of the brown dwarfs in Cha I are compared to the kinematics of T Tauri stars in the same field , based on both UVES measurements for very low-mass ones and on RVs from the literature . More UVES spectra were taken compared with a former paper ( Joergens & Guenther 2001 ) , and the reduction of the spectra was improved , while studying the literature for RVs of T Tauri stars in Cha I led to a cleaned and enlarged sample of T Tauri stars . The result is an improved empirical RV distribution of brown dwarfs , as well as of T Tauri stars in Cha I . We found that the RVs of the nine brown dwarfs and very low-mass stars ( M6–M8 ) in ChaI that were studied have a mean value of 15.7 km s ^ { -1 } and a dispersion measured in terms of a standard deviation of 0.9 km s ^ { -1 } , and they cover a total range of 2.6 km s ^ { -1 } . The standard deviation is consistent with the dispersion measured earlier in terms of fwhm of 2.1 km s ^ { -1 } . The studied sample of 25 T Tauri stars ( G2–M5 ) has a mean RV of 14.7 km s ^ { -1 } , a dispersion in terms of standard deviation of 1.3 km s ^ { -1 } and in terms of fwhm of 3.0 km s ^ { -1 } , and a total range of 4.5 km s ^ { -1 } . The RV dispersion of the brown dwarfs is consistent within the errors with that of T Tauri stars , which is in line with the finding of no mass dependence in some theoretical models of the ejection-scenario for the formation of brown dwarfs . In contrast to current N-body simulations , we did not find a high-velocity tail for the brown dwarfs RVs . We found hints suggesting different kinematics for binaries compared to predominantly single objects in Cha I , as suggested by some models . The global RV dispersion for Cha I members ( 1.24 km s ^ { -1 } ) is significantly lower than for Taurus members ( 2.0 km s ^ { -1 } ) , despite higher stellar density in Cha I showing that a fundamental increase in velocity dispersion with stellar density of the star-forming region is not established observationally . The RVs of brown dwarfs observed in Cha I are less dispersed than predicted by existing models for the ejection-scenario .