In a search for the decay K(L)0 --> e+e-, no candidates have been obse
rved. We determine the sensitivity from the detected number of CP-viol
ating K(L)0 --> pi+pi- decays and place a 90% confidence level upper l
imit on the branching ratio of B(K(L)0 --> e+e-, \M(K) - M(ee)\; < 6 M
eV/c2) less-than-or-equal-to 4.1 x 10(-11). This result is a significa
nt improvement over previous measurements, although still above the st
andard model prediction of 3 x 10(-12).