We observe D(0)-D(0) mixing in the decay D(0) → K+π- using a data sample of integrated luminosity 976 fb(-1) collected with the Belle detector at the KEKB e+e- asymmetric-energy collider. We measure the mixing parameters x'(2) = (0.09 ± 0.22) × 10(-3) and y'=(4.6 ± 3.4) × 10(-3) and the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates R(D) = (3.53 ± 0.13) × 10(-3), where the uncertainties are statistical and systematic combined. Our measurement excludes the no-mixing hypothesis at the 5.1 standard deviation level.