We report on a search for the decay KL-->pi(0)e+e- carried out by the KTeV/E799 experiment at Fermilab. This decay is expected to have a significant CP violating contribution and the measurement of its branching ratio 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 background of 1.06+/-0.41 events, and we set an upper limit B(KL-->pi(0)e+e-)<5.1 x 10(-10) at the 90% confidence level.