  We present a preliminary measurement of the time-dependent CP asymmetry for
the neutral B-meson decay into the CP = +1 final state KS pi0 pi0, with KS->
pi+ pi- and pi0-> gamma gamma. We use a sample of approximately 227 million
B-meson pairs recorded at the Y(4S) resonance by the BaBar detector at the
PEP-II B-Factory at SLAC. From a maximum likelihood fit we extract the
mixing-induced CP-violation parameter S = 0.84 +/- 0.71(stat} +/- 0.08{syst)
and the direct CP-violation parameter C = 0.27 +/- 0.52(stat) +/- 0.13(syst},
where the first uncertainty is statistical and the second systematic.
