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.

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