  The branching ratio of the rare decay pi0 -> e+ e- has been measured
precisely, using the complete data set from the KTeV E799-II experiment at
Fermilab. We observe 794 candidate pi0 -> e+ e- events using K0_L -> 3pi0 as a
source of tagged pi0's. The expected background is 52.7 +- 11.2 events,
predominantly from high e+ e- mass pi0 -> e+ e- gamma decays. We have measured
B[(pi0 -> e+ e-), (m_e+e-/m_pi0)^2 > 0.95] = 6.44 +- 0.25(stat) +- 0.22(syst)
x10^(-8), which is above the unitary bound from pi0 -> gamma gamma and within
the range of theoretical expectations from the standard model.
