We report the first branching fraction measurement of the decay K-L --> pi(+)pi(-) e(+)e(-). With a sample of 46 candidates, and an expected background level of 9.4 events, the branching fraction is determined to be B(K-L --> pi(+)pi(-) e(+)e(-)) = [3.2 +/- 0.6(stat) +/- 0.4(syst)] x 10(-7). This measurement was carried out as part of the Fermilab KTeV (E799-II) experiment and is in good agreement with the expectations from the mechanisms of direct emission and inner bremsstrahlung.