The first observation of the decay Bs -> D0bar K- {pi}+ is reported. The analysis is based on a data sample, corresponding to an integrated luminosity of 1.0 fb-1 of pp collisions, collected with the LHCb detector. The branching fraction relative to that of the topologically similar decay B0 -> D0bar {pi}+ {pi}- is measured to be BR(Bs -> D0bar K- {pi}+)/BR(B0 -> D0bar {pi}+ {pi}-) = 1.18 +- 0.05 (stat.) +- 0.12 (syst.). In addition, the relative branching fraction of the decay B0 -> D0bar K+ {pi}- is measured to be BR(B0 -> D0bar K+ {pi}-)/BR(B0 -> D0bar {pi}+ {pi}-) = 0.106 +- 0.007 (stat.) +- 0.008 (syst.).
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