The suppressed decay chain B- -> DK-, D -> K+pi-, where D indicates a anti-D0 or D0 state, provides important information on the CP-violating angle phi_3. We measure the ratio R_{DK} of the decay rates to the favored mode B- -> DK-, D -> K-pi+ to be R_{DK} = [1.63^{+0.44}_{-0.41}(stat)^{+0.07}_{-0.13}(syst)] x 10^{-2}, which indicates the first evidence of the signal with a significance of 4.1sigma. We also measure the asymmetry A_{DK} between the charge-conjugate decays to be A_{DK} = -0.39^{+0.26}_{-0.28}(stat)^{+0.04}_{-0.03}(syst). The results are based on the full 772 x 10^6 B anti-B pair data sample collected at the Upsilon(4S) resonance with the Belle detector.
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