We report the first observation of a manifestly CP violating effect in the K(L)-->pi(+)pi(-)e(+)e(-) decay mode. A large asymmetry was observed in the distribution of these decays in the CP-odd and T-odd angle straight phi between the decay planes of the e(+)e(-) and pi(+)pi(-) pairs in the K(L) center of mass system. After acceptance corrections, the overall asymmetry is found to be [13.6+/-2. 5(stat)+/-1.2(syst)]%. This is the largest CP-violating effect yet observed when integrating over the entire phase space of a mode and the first such effect observed in an angular variable.