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.
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