P. van Dokkum, Yale University; J. S. Bloom, Harvard- Smithsonian Center for Astrophysics; and C. Bailyn, B. Cobb, and M. Buxton, Yale University, report further analysis of SMARTS- consortium data on GRB 031203 (cf. GCN 2463) obtained between Dec. 4.125 and 4.258 UT. The summed images reveal no source in I or J (upper magnitude limits I = 23 and J = 21.0) at the Rapid-Eye-Mount (REM) robotic-telescope position from La Silla (cf. GCN 2466). A faint source with J = 20.5 +/- 0.5, undetectable in I, is found 2.5 from the REM position at R.A. = 8h02m29s.78, Decl. = -39o51'07''.1 (equinox 2000.0) +/- 0.4 (1 sigma; found from astrometric tie to 2MASS). No other source is found within 4’'.5 of the REM position. The J-band data were obtained starting at Dec. 4.180 (essentially contemporaneous with the REM observations), while the I-band images span the entire three hours of observation. Taking the REM and SMARTS photometry at face value, it is found that the source has the characteristics of a J ‘dropout’, suggesting a redshift of z > 9 (formally z >/= 11). Models assuming extreme extinction in the host galaxy cannot reproduce the observed spectral energy distribution (see http://www.astro.yale.edu/dokkum/GRB031203.html). There are many caveats, and the nature of this source is still highly uncertain. Nevertheless, as this is a potential discovery of the highest redshift source known, the authors encourage the community to obtain additional near-infrared photometry and (particularly) near- infrared spectroscopy of this object.