We report on a search for the decay K-L --> pi (0)e(+)e(-) carried out by t
he KTeV/E799 experiment. at Fermilab. This decay is expected to have a sign
ificant CP violating contribution and the measurement of its branching rati
o could support the Cabibbo-Kobayashi-Maskawa mechanism for CP violation or
could point to new physics. Two events were observed in the 1997 data with
an expected back ground of 1.06 +/- 0.41 events, and we set an upper limit
B(K-L --> pi (0)e(+)e(-)) <5.1 X 10(-10) at the 90% confidence level.