We observe D-0-(D) over bar (0) mixing in the decay D-0 -> K+ pi(-) 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) x 10(-3) and y' = (4.6 +/- 3.4) x 10(-3) and the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates R-D = (3.53 +/- 0.13) x 10(-3) where the uncertainties are statistical and systematic combined. Our measurement excludes the no-mixing hypothesis at the 5.1 standard deviation level.