The first observation of the decay B0 -> D0bar K+ K- is reported from an analysis of 0.62 fb-1 of pp collision data collected with the LHCb detector. Its branching fraction is measured relative to that of the topologically similar decay B0 -> D0bar pi+ pi- to be BR(B0 -> D0bar K+ K-)/BR(B0 -> D0bar pi+ pi-) = 0.056+-0.011+-0.007, where the first uncertainty is statistical and the second is systematic. The significance of the signal is 5.8 sigma. Evidence, with 3.8 sigma significance, for Bs -> D0bar K+ K- decays is also presented, with a relative branching fraction of BR(Bs -> D0bar K+ K-)/BR(B0 -> D0bar K+ K-) = 0.90+-0.27+-0.20.
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