We present deep near-infrared (JSHKS) imaging observations, carried out with the ESO Very Large Telescope (VLT), of a field in the Chamaeleon I star forming region in an attempt to identify possible members with masses comparable to, or below, the mass of Jupiter. We focus on an object, Cha I J110814.2-773649, which stands out as an outlier in color-color and color-magnitude diagrams of the field, with H=22.16+0.21-0.17, H-KS=-0.01+0.26-0.24, and JS-H=2.00+∞-0.62. H-band spectroscopy of this object shows that the unusual colors are not due to emission lines in the region; furthermore, this spectroscopy allows clear detection of the object's continuum. Assuming membership in Chamaeleon I and an age of 2 Myr (the age of most members of Cha I), the blue H-KS color and the absolute magnitude are consistent with model predictions for a cool, sub-Jupiter mass object with strong dust depletion in the atmosphere. However, the very red JS-H color implied by the marginal detection in the JS band is unexpected in an object with such atmospheric properties. We speculate that this might be due to differences in the properties of dust and its depletion under the photosphere with respect to field objects (T dwarfs) that have a similar temperature, these differences resulting from both the youth and the low surface gravity of a low-mass member of a star-forming region. We also consider the alternative possibility that Cha I J110814.2-773649 might actually be a high-redshift object, whose red JS-H color could result from absorption of the flux blueward of Lyα in the J band. We find that this possibility would be marginally compatible with the JSHKS photometry of Cha I J110814.2-773649 if it were an unreddened starburst at 8.5<z<11.Based on observations obtained at the European Southern Observatory using the Very Large Telescope, Cerro Paranal, Chile (programmes 64.L-0049[A] and 67.C-0109[B]).