Abstract: The first observation of the B-s(0) -> (D) over bar K-0 (+) K- decay is reported, together with the most precise branching fraction measurement of the mode B-0 -> (D) over bar K-0 (+) K- The results are obtained from an analysis of pp collision data corresponding to an integrated luminosity of 3.0 fb(-1). The data were collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, The branching fraction of the B-0 -> (D) over bar K-0 (+) K- decay is measured relative to that of the decay B-0 -> (D) over bar (0)pi (+) pi(-) to be B(B-0 -> (D) over bar K-0 (+) K-)/B(B-0 -> (D) over bar (0)pi (+) pi(-)) =(69 +/- 0.4 +/- 0.3)%, where the first uncertainty is statistical and the second is systematic. The measured branching fraction of the B-s(0) -> (D) over bar K-0 (+) K- decay mode relative to that of the corresponding B-0 decay is B(B-0 -> (D) over bar K-0 (+) K-)/B(B-0 -> (D) over bar K-0 (+) K-) = (93.0 +/- 809 +/- 6.9)%. Using the known branching fraction of B-0 -> (D) over bar (0)pi (+) pi(-), the values of B-0 -> (D) over bar K-0 (+) K- = (6.1 +/- 0.4 +/- 0.3 +/- 0.3) x 10(-5) and B(B-s(0) -> (D) over bar K-0 (+) K- = (5.7 +/- 0.5 +/- 0.4 +/- 0.5) x 10(-5) are obtained, where the third uncertainties arise from the branching fraction of the decay modes B-0 -> (D) over bar (0)pi (+) pi(-) and B-0 -> (D) over bar K-0 (+) K-, respectively.