  We have observed four fully reconstructed B0 -> D*+D*- candidates in 5.8
million Upsilon(4S) -> BBbar decays recorded with the CLEO detector. The
background is estimated to be 0.31 +- 0.10 events. The probability that the
background could produce four or more signal candidates with the observed
distribution among D*+ and D*- decay modes is 1.1 X 10^{-4}. The measured decay
rate, Br(B0 -> D*+D*-) = [6.2 +4.0-2.9 (stat) +- 1.0(syst)] X 10^{-4}, is large
enough for this decay mode to be of interest for the measurement of a
time-dependent CP asymmetry.
