We measure the time dependence of the ratio of decay rates for D0 -> K+ pi- to the Cabibbo-favored decay D0 -> K- pi+. The charge conjugate decays are included. A signal of 3.3 x 10^4 D*+ -> pi+ D0, D0 -> K+ pi- decays is obtained with D0 proper deca
y times between 0.75 and 10 mean D0 lifetimes. The data were recorded with the CDF II detector at the Fermilab Tevatron and correspond to an integrated luminosity of 9.6 fb-1 for p-pbar collisions at sqrt(s) = 1.96 TeV. Assuming CP conservation, we search for D0-D0bar mixing and measure the mixing parameters to be R_D = (3.51 +/- 0.35) x 10^{-3}, y = (4.3 +/- 4.3) x 10^{-3}, and x^2 = (0.08 +/- 0.18) x 10^{-3}. We report Bayesian probability intervals in the x^2 - y plane and find that the significance of excluding the no-mixing hypothesis is equivalent to 6.1 Gaussian standard deviations, providing the second observation of D0-D0bar mixing from a single experiment.
