We present a measurement of B(π0→e+e−γ)/B(π0→γγ), the Dalitz branching ratio, using data taken in 1999 by the E832 KTeV experiment at Fermi National Accelerator Laboratory. We use neutral pions from fully reconstructed KL decays in flight; the measurement is based on ∼60 thousand KL→π0π0π0→γγγγe+e−γ decays. We normalize to KL→π0π0π0→6γ decays. We find B(π0→e+e−γ)/B(π0→γγ) (me+e−>15  MeV/c2)=3.920±0.016(stat)±0.036(syst)×10−3. Using the Mikaelian and Smith prediction for the e+e− mass spectrum, we correct the result to the full e+e− mass range. The corrected result is B(π0→e+e−γ)/B(π0→γγ)=1.1559±0.0047(stat)±0.0106(syst)%. This result is consistent with previous measurements, and the uncertainty is a factor of 3 smaller than any previous measurement.