We observe evidence for D-0-(D) over bar (0) mixing by measuring the difference in the apparent lifetime when a D-0 meson decays to the CP eigenstates K+K- and pi(+)pi(-) and when it decays to the final state K-pi(+). We find the relative difference of the lifetimes y(CP) to be [1.31 +/- 0.32(stat)+/- 0.25(syst)]%, 3.2 standard deviations from zero. We also search for a CP asymmetry between D-0 and (D) over bar (0) decays; no evidence for CP violation is found. These results are based on 540 fb(-1) of data recorded by the Belle detector at the KEKB e(+)e(-) collider.