Characterization of a Kodak KAF 4200 CCD chip, coated with the UV converter Lumigen, is described. This chip is very similar to a chip described by Ninkov, Backer, and Bretz [Proc. SPIE1987, 14 (1993)], except for the Lumigen coating. The major difference in perlormance is in the existence of significant deviations from linear output for a given input up to 30% at low count rates. The nonlinearity varies across the chip and is largest for pixels that are the most distant from the readout serial register. Tests revealed that the nonlinearity depends on wavelength in a minor way only, and is temperature dependent. Characterization of the nonlinearity allowed the creation of a function that allows for correction of the data. It is unlikely that this nonlinearity can be explained using arguments invoking deferred charge effects or peculiar behavior of the on-chip amplifier. Comparison with similar but uncoated CCD chips makes the Lumigen coating a likely source of the problem.