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Chamaeleon I is the most active region in terms of star formation in theChamaeleon molecular cloud complex. Its population of prestellar andprotostellar cores is not known and a controversy exists concerning its historyof star formation. Our goal is to characterize the earliest stages of starformation in this cloud. We used the bolometer array LABOCA at APEX to map thecloud in dust continuum emission at 870 micron. The detected sources areanalysed by carefully taking into account the spatial filtering inherent in thedata reduction process. A search for associations with YSOs is performed usingSpitzer data and the SIMBAD database. Most of the detected 870 micron emissionis distributed in 5 filaments. We identify 59 starless cores, one candidatefirst hydrostatic core, and 21 sources associated with more evolved YSOs. Thestarless cores are only found above a visual extinction threshold of 5 mag.They are less dense than those detected in other nearby molecular clouds by afactor of a few on average. The core mass distribution is consistent with theIMF at the high-mass end but is overpopulated at the low-mass end. In addition,at most 17% of the cores have a mass larger than the critical Bonnor-Ebertmass. Both results suggest that a large fraction of the starless cores may notbe prestellar. Based on the census of prestellar cores, Class 0 protostars, andmore evolved YSOs, we conclude that the star formation rate has decreased withtime in this cloud. The low fraction of candidate prestellar cores among thepopulation of starless cores, the small number of Class 0 protostars, the highglobal star formation efficiency, the decrease of the star formation rate withtime, and the low mass per unit length of the detected filaments all suggestthat we may be witnessing the end of the star formation process in Cha I{abridged}.

The end of star formation in Chamaeleon I ? A LABOCA census of starless and protostellar cores