We have studied twelve very young (1–5 Myr) bona fide and candidate brown dwarfs in the Cha I star forming region in terms of their kinematic properties, the occurrence of multiple systems among them as well as their rotational characteristics. Based on high-resolution spectra taken with UVES at the VLT (8.2 m), radial and rotational velocities have been measured. A kinematic study of the sample showed that their radial velocity dispersion is relatively small suggesting that they are not ejected during their formation as proposed in recent formation scenarios. By means of time-resolved UVES spectra, a radial velocity survey for close companions to the targets was conducted. The radial velocities of the targets turned out to be rather constant setting upper limits for the mass M2 sin i of possible companions to 0.1 MJup – 2 MJup. These findings hint at a rather low (≤ 10%) multiplicity fraction of the studied brown dwarfs. Furthermore, a photometric monitoring campaign of the targets yielded the determination of rotational periods for three brown dwarf candidates in the range of 2.2 to 3.4 days. These are the first rotational periods for very young brown dwarfs and among the first for brown dwarfs at all.