  SONYC - Substellar Objects in Nearby Young Clusters - is a survey program to
investigate the frequency and properties of substellar objects with masses down
to a few times that of Jupiter in nearby star-forming regions. In this third
paper, we present our recent results in the Chamaeleon-I star forming region.
We have carried out deep optical and near-infrared imaging in four bands (I, z,
J, Ks) using VIMOS on the ESO Very Large Telescope and SOFI on the New
Technology Telescope, and combined our data with mid-infrared data from the
Spitzer Space Telescope. The survey covers ~0.25 sqdeg on the sky, and reaches
completeness limits of 23.0 in the I-band, 18.3 in the J-band, and 16.7 in
Ks-band. Follow-up spectroscopy of the candidates selected from the optical
photometry (I <~ 21) was carried out using the multi-object spectrograph VIMOS
on the VLT. We identify 13 objects consistent with M spectral types, 11 of
which are previously known M-dwarfs with confirmed membership in the cluster.
The 2 newly reported objects have effective temperatures above the substellar
limit. We also present two new candidate members of Chamaeleon-I, selected from
our JK photometry combined with the Spitzer data. Based on the results of our
survey, we estimate that the number of missing very-low-mass members down to
~0.008 MSun and Av <= 5 is <= 7, i.e. <= 3% of the total cluster population
according to the current census.
