The suppressed decay chain B- -> DK-, D -> K+pi(-), where D indicates a (D) over bar (0) or D-0 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(-0.41)(+0.44)(stat)(-0.13)(+0.07)(syst)] x 10(-2), which indicates the first evidence of the signal with a significance of 4.1 sigma. We also measure the asymmetry A(DK) between the charge-conjugate decays to be A(DK) = -0.39(-0.28)(+0.26)(stat)(-0.03)(+0.04)(syst). The results are based on the full 772 x 10(6) B (B) over bar pair data sample collected at the Gamma(4S) resonance with the Belle detector.