The Chamaeleon clouds are excellent targets for low-mass star formation studies. Cha I and II are actively forming stars while Cha III shows no sign of ongoing star formation. We aim to determine the driving factors that have led to the very different levels of star formation activity in Cha I and III and examine the dynamical state and possible evolution of the starless cores within them. Observations were performed in various molecular transitions with APEX and Mopra. Five cores are gravitationally bound in Cha I and one in Cha III. The infall signature is seen toward 8-17 cores in Cha I and 2-5 cores in Cha III, which leads to a range of 13-28% of the cores in Cha I and 10-25% of the cores in Cha III that are contracting and may become prestellar. Future dynamical interactions between the cores will not be dynamically significant in either Cha I or III, but the subregion Cha I North may experience collisions between cores within ~0.7 Myr. Turbulence dissipation in the cores of both clouds is seen in the high-density tracers N2H+ 1-0 and HC3N 10-9. Evidence of depletion in the Cha I core interiors is seen in the abundance distributions of C17O, C18O, and C34S. Both contraction and static chemical models indicate that the HC3N to N2H+ abundance ratio is a good evolutionary indicator in the prestellar phase for both gravitationally bound and unbound cores. In the framework of these models, we find that the cores in Cha III and the southern part of Cha I are in a similar evolutionary stage and are less chemically evolved than the central region of Cha I. The measured HC3N/N2H+ abundance ratio and the evidence for contraction motions seen towards the Cha III starless cores suggest that Cha III is younger than Cha I Centre and that some of its cores may form stars in the future. The cores in Cha I South may on the other hand be transient structures. (abridged)
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