We observe evidence for D(0)-D(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(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.