We have searched for B_{s}^{0}->hh decays, where h stands for a charged or neutral kaon, or a charged pion. These results are based on a 23.6 fb^{-1} data sample collected with the Belle detector on the \Upsilon(5S) resonance at the KEKB asymmetric-energy e^{+}e^{-} collider, containing 1.25x10^6 B_{s}^{()}\bar{B}_{s}^{()} events. We observe the decay B_{s}^{0}->K^{+}K^{-} and measure its branching fraction, (B_{s}^{0}->K^{+}K^{-}) = [3.8_{-0.9}^{+1.0}()\pm 0.5()\pm 0.5(f_s)] \times 10^{-5}. The first error is statistical, the second is systematic, and the third error is due to the uncertainty in the B^0_s production fraction in events. No significant signals are seen in other decay modes, and we set upper limits at 90% confidence level: (B_{s}^{0}->K^-\pi^{+})< 2.6 \times 10^{-5}, (B_{s}^{0}->\pi^{+}\pi^{-})< 1.2 \times 10^{-5} and (B_{s}^{0}->K^0\bar{K}^0) < 6.6\times 10^{-5}.

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