Using the CLEO detector at the Cornell Electron Storage Ring we have observed the Omega(c)(0) (css ground state) in the decay Omega(c)(0) --> 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(c)(0) --> Omega(-)e(+)nu(e)).sigma(e(+)e(-) --> Omega(c)(0)X) = (42.2 +/- 14.1(stat) +/- 5.7(syst)) fb and R = Gamma(Omega(c)(0)Omega(-)--> pi(+))/Gamma(Omega(c)(0) --> 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(c)(0) 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.