  We report the results of the first search for the decay $B_s^0 \to
\eta^\prime K_S^0$ using $121.4\,{\rm fb}^{-1}$ of data collected at the
$\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy
$e^+ e^-$ collider. We observe no signal and set a 90\% confidence-level upper
limit of $8.16 \times 10^{-6}$ on the $B_s^0 \to \eta^\prime K_S^0$ branching
fraction.
