  We present a new measurement of the time-dependent CP asymmetry of B0->D*+D*-
decays using (471+-5) million BBbar pairs collected with the BaBar detector at
the PEP-II B Factory at the SLAC National Accelerator Laboratory. Using the
technique of partial reconstruction, we measure the time-dependent CP asymmetry
parameters S=-0.34+-0.12+-0.05$ and C=+0.15+-0.09+-0.04. Using the value for
the CP-odd fraction R_perp=0.158+-0.028+-0.006, previously measured by BaBar
with fully reconstructed B0->D*+D*- events, we extract the CP-even components
S+=-0.49+-0.18+-0.07+-0.04 and C+=+0.15+-0.09+-0.04. In each case, the first
uncertainty is statistical and the second is systematic; the third uncertainty
on S+ is the contribution from the uncertainty on R_perp. The measured value of
the CP-even component S+ is consistent with the value of sin(2Beta) measured in
b->(ccbar)s transitions, and with the Standard Model expectation of small
penguin contributions.
