Deep CCD photometry and positions for a new sample of similar or equal to 250 dwarf elliptical (dE) galaxies in the Coma cluster core are analyzed. A significant color gradient is detected in their projected radial distribution, given by Delta(B-R)/Delta(logR(proportional to)) = -0.08 +/- 0.02 mag. Calibrating these dE galaxies against Galactic globular dusters yields a corresponding metallicity gradient which goes as Z proportional to R(proportional to)(-0.29). Simulations reveal that this gradient in the projected radial distribution corresponds to a true (three-dimensional) radial color gradient which goes as Delta(B-R)/Delta(log r)similar or equal to -0.20 mag, or Z proportional to r(-0.69), over the same radial range. If this radial gradient is a primordial one, it is consistent with a model in which the intracluster gas exerted a significant confinement pressure, impeding the outflow of supernovae-driven metal-rich gas from the young dE galaxies.