The B^0_s-bar{B}^0_s oscillation frequency Delta m_s is measured with 36 pb^{-1} of data collected in pp collisions at sqrt{s} = 7 TeV by the LHCb experiment at the Large Hadron Collider. A total of 1381 B^0_s -> D_s^- pi^+ and B^0_s -> D_s^- pi^+ pi^- pi^+ signal decays are reconstructed, with average decay time resolutions of 44 fs and 36 fs, respectively. An oscillation signal with a statistical significance of 4.6 sigma is observed. The measured oscillation frequency is Delta m_s = 17.63 pm 0.11 (stat) pm 0.02 (syst) ps^{-1}.
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