We observe evidence for D0-D̄0 mixing by measuring the difference in the apparent lifetime when a D0 meson decays to the CP eigenstates K+K- and π+π- and when it decays to the final state K-π+. We find the relative difference of the lifetimes yCP to be [1.31±0.32(stat)±0.25(syst)] %, 3.2 standard deviations from zero. We also search for a CP asymmetry between D0 and D̄0 decays; no evidence for CP violation is found. These results are based on 540fb-1 of data recorded by the Belle detector at the KEKB e+e- collider. © 2007 The American Physical Society.