  Context: Chamaeleon is the southernmost low-mass star-forming complex within
200 pc from the Sun. Its stellar population has been extensively studied in the
past, but the current census of the stellar content is not complete yet and
deserves further investigation.
  Aims: We take advantage of the second data release of the \textit{Gaia} space
mission to expand the census of stars in Chamaeleon and to revisit the
properties of the stellar populations associated to the Chamaeleon I (Cha I)
and Chamaeleon II (Cha II) dark clouds.
  Methods: We perform a membership analysis of the sources in the \textit{Gaia}
catalogue over a field of 100 deg$^{2}$ encompassing the Chamaeleon clouds, and
use this new census of cluster members to investigate the 6D structure of the
complex.
  Results: We identify 188 and 41 high-probability members of the stellar
populations in Cha I and Cha II, respectively, including 19 and 7 new members.
Our sample covers the magnitude range from $G=6$ to $G=20$ mag in Cha I, and
from $G=12$ to $G=18$ mag in Cha II. We confirm that the northern and southern
subgroups of Cha I are located at different distances ($191.4^{+0.8}_{-0.8}$ pc
and $186.7^{+1.0}_{-1.0}$ pc), but they exhibit the same space motion within
the reported uncertainties. Cha II is located at a distance of
$197.5^{+1.0}_{-0.9}$ pc and exhibits a space motion that is consistent with
Cha I within the admittedly large uncertainties on the spatial velocities of
the stars that come from radial velocity data. The median age of the stars
derived from the Hertzsprung-Russell diagram (HRD) and stellar models is about
1-2 Myr, suggesting that they are somewhat younger than previously thought. We
do not detect significant age differences between the Chamaeleon subgroups, but
we show that Cha II exhibits a higher fraction of disc-bearing stars compared
to Cha I.
