We have searched for the rare decay of the eta meson eta-->e(+)e(-) us
ing the CLEO II detector. The eta's were produced in e(+)e(-) collisio
ns with 10 GeV center-of-mass energy at the Cornell Electron Storage R
ing (CESR). We find with 90% confidence the upper limit on the branchi
ng fraction B(eta-->e(+)e(-))<7.7x10(-5). The application of conventio
nal elementary particle theory to this decay predicts a branching frac
tion of about 10(-9).