  We present an Atacama Large Millimeter/submillimeter Array (ALMA) 106 GHz
(Band 3) continuum survey of the complete population of dense cores in the
Chamaeleon I molecular cloud. We detect a total of 24 continuum sources in 19
different target fields. All previously known Class 0 and Class I protostars in
Chamaeleon I are detected, whereas all of the 56 starless cores in our sample
are undetected. We show that the Spitzer+Herschel census of protostars in
Chamaeleon I is complete, with the rate at which protostellar cores have been
misclassified as starless cores calculated as <1/56, or < 2%. We use synthetic
observations to show that starless cores collapsing following the turbulent
fragmentation scenario are detectable by our ALMA observations when their
central densities exceed ~10^8 cm^-3, with the exact density dependent on the
viewing geometry. Bonnor-Ebert spheres, on the other hand, remain undetected to
central densities at least as high as 10^10 cm^-3. Our starless core
non-detections are used to infer that either the star formation rate is
declining in Chamaeleon I and most of the starless cores are not collapsing,
matching the findings of previous studies, or that the evolution of starless
cores are more accurately described by models that develop less substructure
than predicted by the turbulent fragmentation scenario, such as Bonnor-Ebert
spheres. We outline future work necessary to distinguish between these two
possibilities.
