  We report the first direct measurement of the inclusive branching fraction
${\mathcal B}(B_s \rightarrow D_s X)$ via $B_s$ tagging in
$e^+e^-\to\Upsilon$(5S) events. Tagging is accomplished through a partial
reconstruction of semileptonic decays $B_s \rightarrow D_s X \ell \nu$, where
$X$ denotes unreconstructed additional hadrons or photons and $\ell$ is an
electron or muon. With 121.4 fb$^{-1}$ of data collected at the $\Upsilon$(5S)
resonance by the Belle detector at the KEKB asymmetric-energy $e^+ e^-$
collider, we obtain ${\mathcal B}(B_s \rightarrow D_s X)$ = $(60.2 \pm 5.8 \pm
2.3)$\%, where the first uncertainty is statistical and the second is
systematic.
