Using the CLEO detector at the Cornell Electron Storage Ring we have observed the Omega(0)(c) (css ground state) in the decay Omega(0)(c)-->Omega(-)e(+)nu(e). We find a signal of 11.4+/-3.8(stat) events. The probability that we have observed a background fluctuation is 7.6x10(-5). We measure B(Omega(0)(c)-->Omega(-)e(+)nu(e)).sigma(e(+)e(-)-->Omega(0)(c)X)=(42.2+/-14.1(stat)+/-5.7(syst)) fb and R=[Gamma(Omega(0)(c)-->Omega(-)pi(+))]/[Gamma(Omega(0)(c)-->Omega(-)enu(e))]=00.41+/-0.19(stat)+/-0.04(syst). This is the first statistically significant observation of an individual decay mode of the Omega(0)(c) in e(+)e(-) annihilation and the first example of a baryon decaying via beta emission, where no quarks from the first generation participate in the reaction.