  The first observation of the $B^0_s \to D_s^{*\mp} K^{\pm}$ decay is reported
using 3.0$fb^{-1}$ of proton-proton collision data collected by the LHCb
experiment. The $D_s^{*\mp}$ mesons are reconstructed through the decay chain
$D_s^{*\mp} \to \gamma D_s^{\mp}(K^{\mp}K^{\pm}\pi^{\mp})$. The branching
fraction relative to that for $B^0_s \to D_s^{*-} \pi^{+}$ is measured to be
$0.068 \pm 0.005 ^{+0.003}_{-0.002}$, where the first uncertainty is
statistical and the second is systematic. Using a recent measurement of
$BR(B^0_s \to D_s^{*-} \pi^{+})$ the absolute branching fraction of $B^0_s \to
D_s^{*\mp} K^{\pm}$ is measured as ( 16.3 $\pm$ 1.2 (stat) $^{+0.7}_{-0.5}$
(syst) $\pm$ 4.8 (norm) ) $\times$ 10$^{-5}$, where the third uncertainty is
due to the uncertainty on the branching fraction of the normalisation channel.
