We present deep near-infrared (J_SHK_S) 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, H-K_S = -0.01, and J_S-H = 2.00. 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-K_S 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 J_S-H color implied by the marginal detection in the J_S 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 J_S-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 J_SHK_S photometry of Cha I J110814.2-773649 if it were an unreddened starburst at 8.5 < z < 11.