The branching ratio of the rare decay pi(0) --> e(+)e(-) has been measured in E799-II, a rare kaon decay experiment using the KTeV detector at Fermilab. We observed 275 candidate pi(0) --> e(+)e(-) events, with an expected background of 21.4 +/- 6.2 events which includes the contribution from Dalitz decays. We measured B[pi(0) --> e(+)e(-), (m(e+e-)/m(pi 0))(2) > 0.95] = (6.09 +/- 0.40 +/- 0.24) X 10(-8), where the first error is statistical and the second systematic. This result is the first significant observation of the excess rate for this decay above the unitarity lower bound.