We present the first deep color-magnitude diagram of the putative central region (05 × 05) of the Canis Major stellar overdensity (l, b) = (240, - 8) found recently by Martin and coworkers, which has been proposed as the remnant of a dwarf satellite accreted onto the Milky Way on a near-equatorial orbit. We find a narrow (in apparent magnitude) main sequence extending 6 mag below the turnoff to our limiting magnitude of B ~ 24.5 mag. This main sequence has very high contrast (>3) with respect to the thin/thick disk/halo background; its narrowness at brighter magnitudes clearly implies the presence of a distinct and possibly still bound stellar system. We derived the line-of-sight size (r_1/2) of this system based on the B-band width of the lower main sequence, obtaining 0.94 ± 0.18 (random) ± 0.18 (systematic) kpc. That size matches a model prediction for the main body of the parent galaxy of the Monoceros tidal stream. The high-density contrast and limited spatial extent in the radial direction are very hard to reconcile with the alternative explanation put forward to explain the Canis Major stellar overdensity: a flared or warped Galactic disk viewed in projection, as found in the recent work of Momany and coworkers. We also derived a central surface brightness of μ_V,0 = 23.3 ± 0.1 mag arcsec^-2 and an absolute magnitude of M_V = -14.5 ± 0.1 mag. These values place the Canis Major object in the category of dwarf galaxy, considering the L_V-size and M_V - μ_V planes for such objects. However, like the Sagittarius dwarf, it is an outlier in the [Fe/H] - M_V plane in the sense that it is too metal-rich for its estimated absolute magnitude. This suggests that the main mechanism driving its recent and current star formation history (possibly tidal stripping) is different from that of isolated dwarfs.