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 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.