**Table 1:** Parameters derived from UVES spectra: mean heliocentric radial velocity RV in [kms^-1], projected rotational velocity $v\,\sin i$ and equivalent width EW of lithium (6708Å). Last columns: (sub)stellar radii and upper limits for rotational periods.
object	RV	$v\,\sin i$	EW(Li)	$R_{\star}$	$P_{\rm max}$
	$\pm$ 0.2	[kms^-1]	[Å]	[ $R_{\odot}$ ]	[d]
ChaH $\alpha$ 1	15.5	$7.6\pm2.2$	$0.14 \pm0.10$	0.46	3.1
ChaH $\alpha$ 2	15.4	$12.8\pm1.2$	$0.30 \pm0.08$	0.73	2.9
ChaH $\alpha$ 3	14.2	$21.0\pm1.6$	$0.26 \pm0.08$	0.77	1.9
ChaH $\alpha$ 4	15.4	$18.0\pm2.3$	$0.46 \pm0.11$	0.89	2.5
ChaH $\alpha$ 5	15.5	$15.4\pm1.8$	$0.44 \pm0.10$	0.83	2.7
ChaH $\alpha$ 6	16.1	$13.0\pm2.8$	$0.32 \pm0.08$	0.68	2.6
ChaH $\alpha$ 7	13.7	$\leq$ 10	$\leq$ 0.09	0.37	$\geq$ 1.9
ChaH $\alpha$ 8	14.5	$15.5\pm2.6$	$0.33 \pm0.15$	0.59	1.9
ChaH $\alpha$ 12	13.8	$25.7\pm2.6$	$0.37 \pm0.10$	0.66	1.3
B34	16.5	$15.2\pm1.9$	$0.60 \pm0.13$
CHXR74	15.1	$14.1\pm1.6$	$0.63 \pm0.04$
Sz23	15.8	$17.3\pm3.4$	$0.31 \pm0.08$

Neuhäuser & Comerón (1999) determined a mean RV of $\sim$ 14.6kms^-1 and a total range of 11kms^-1for ChaH $\alpha$ 1 to 8 from medium resolution spectra. The measurements of precise RVs for ChaH $\alpha$ 1 to 8 and ChaH $\alpha$ 12 with UVES allow us to study the kinematics of these bona fide and candidate brown dwarfs with high accuracy. We find that their RVs lie close together, only spanning a range of 2.4kms^-1. The mean RV is 14.9kms^-1 and the RV dispersion is 2.0 kms^-1 (cp. Table1 and Fig.2).

The ChaH $\alpha$ objects are located at the periphery of one of the six cloud cores (No.5) in ChaI in a region with a relatively high density of young stellar objects. The mean RV of the molecular gas of the ChaI cloud and also of the cloud core No.5 is 15.3kms^-1 (Mizuno et al. 1999). The mean RV of the studied brown dwarfs is consistent with this velocity of the gas and therefore with the objects being kinematic members of ChaI. Mizuno et al. determined the RV dispersion of the gas of core No.5 to 1.2kms^-1. The brown dwarfs show a slightly larger RV dispersion (2.0kms^-1) than the surrounding molecular gas but basically reflect the motion of the gas.

The relatively small RV dispersion of the studied bona fide and candidate brown dwarfs gives suggestive evidence that there is no run-away brown dwarf among them. We cannot rule out that some of them have a larger space velocity dispersion since RVs are tracing only space motions in one dimension. Nevertheless our finding indicates that the majority of the nine ChaH $\alpha$ objects are not ejected with high velocities out of a dense region as proposed in formation scenarios (Sterzik & Durisen 1999; Reipurth & Clarke 2001). Some or all of the brown dwarfs may still have been "ejected'' with less than escape velocity into an extended orbit around another component of a multiple system. None of the studied brown dwarfs is closer to a known T Tauri star than 4600AU, i.e. it is unlikely that one of them is still bound to a star. There is still the possibility that the parent star itself was later ejected with escape velocity and left an unbound brown dwarf.

**Table 2:** List of T Tauri stars in ChaI with known RVs with a precision of 2kms^-1 or better from: ¹ Dubath et al. (1996), ² Covino et al. (1997), ³ Guenther et al., in prep. and from UVES observations (B34, CHXR74, Sz23: see Table1).
object	RV [kms^-1]	$v\,\sin i$ [kms^-1]
Sz4¹	$16.5 \pm1.3$	$16.6 \pm3.3$
Sz6¹	$14.9 \pm0.8$	$38.0 \pm1.5$
Sz9¹	$14.7 \pm0.3$	$15.2 \pm1.5$
Sz11¹	$15.1 \pm0.5$	$16.2 \pm2.3$
Sz15¹	$17.2 \pm0.6$	4.9 $\pm <$ 7.9
Sz19¹	$13.5 \pm0.6$	$35.7 \pm1.1$
Sz20¹	$15.4 \pm1.3$	$23.9 \pm2.7$
Sz36¹	$12.9 \pm0.9$	7.5 (+2.7-4.8)
Sz41¹	$13.9 \pm0.4$	$34.4 \pm1.4$
Sz42¹	$15.1 \pm0.3$	$27.2 \pm1.3$
RXJ1109.4-7627²	$13.1 \pm2.0$	$14.5 \pm3$
B33² (CHXR25)	$13.0 \pm2.0$	-
F34²	$14.0 \pm2.0$	$55 \pm3$
RXJ1111.7-7620²	$19.0 \pm2.0$	$23 \pm3$
RXJ1112.7-7637²	$16.0 \pm2.0$	$11 \pm3$
CS Cha³	14.9
CT Cha³	$15.5 \pm1.4$
CV Cha³	$15.6 \pm0.9$
SX Cha³	$13.4 \pm0.9$
SY Cha³	$12.7 \pm0.1$
TW Cha³	$15.7 \pm1.2$
VW Cha³	$15.1 \pm0.1$
VZ Cha³	14.7
WY Cha³	12.1

We compared the RV distribution of the bona fide and candidate brown dwarfs also with those of T Tauri stars. Radio observations by Mizuno et al. (1999) revealed that the three main clouds in the Chamaeleon star forming region differ to a large extent in their star formation properties and also the RVs of the molecular gas vary between the clouds (differences up to 3.6km^-1), whereas they are relatively constant ( $\sim$ 1kms^-1) within each single cloud. Therefore it is reasonable to compare the kinematics of the brown dwarfs in ChaI with those of T Tauri stars also confined to the ChaI star forming cloud.

RVs of T Tauri stars in ChaI have been measured by Dubath et al. (1996), Covino et al. (1997), Neuhäuser & Comerón (1999) and by us and are listed in Table2. Furthermore unpublished RVs of T Tauri stars based on FEROS spectra have been included (Guenther et al., in prep.). The T Tauri stars have RVs in the range of [12.1 $\dots$ 19.0kms^-1] with a mean RV of 14.9kms^-1 and a dispersion of 3.6kms^-1 (cp. Fig.2).

The mean RV of the T Tauri stars matches very well the ones of the bona fide and candidate brown dwarfs in ChaI, whereas the dispersion as well as the total range of RVs of the T Tauri stars is significantly larger than the ones of the brown dwarfs. The stellar activity of T Tauri stars probably account for this discrepancy since it has been shown that T Tauri stars exhibit a "RV noise'' of the order of $\sim$ 2kms^-1 due to stellar activity (Guenther et al. 2000). Moreover it may also play a role that the brown dwarfs and brown dwarf candidates are all situated in a small area at the periphery of one cloud core whereas the T Tauri stars are distributed over the whole ChaI region. The RVs of the six cloud cores within ChaI differ by $\pm$ 0.25kms^-1 (Mizuno et al. 1999).

4 Kinematics of brown dwarfs and T Tauri stars in the ChaI cloud