  We present a measurement of the time-dependent CP-violating asymmetries in
$B^0 \to K^{*0}\gamma (K^{*0}\to K_S^0 \pi^0)$ decays based on 124 million
$\Upsilon(4S)\to B^0\bar{B}^0$ decays collected with the BaBar detector at the
PEP-II asymmetric-energy $B$ Factory at the Stanford Linear Accelerator Center.
In a sample containing $105\pm 14$ signal decays, we measure $S_{K^{*0}} = 0.25
\pm 0.63 \pm 0.14$ and $S_{K^{*0}} = -0.57 \pm 0.32 \pm 0.09$, where the first
error is statistical and the second systematic.
