We present a measurement of D 0 − ¯¯¯ D 0 mixing and C P violation using the ratio of lifetimes simultaneously extracted from a sample of D 0 mesons produced through the flavor-tagged process D * + → D 0 π + , where D 0 decays to K ∓ π ± , K − K + , or π − π + , along with the untagged decays D 0 → K ∓ π ± and D 0 → K − K + . The lifetimes of the C P -even, Cabibbo-suppressed modes K − K + and π − π + are compared to that of the C P -mixed mode K ∓ π ± in order to measure y C P and Δ Y . We obtain y C P = [ 0.72 ± 0.18 ( stat ) ± 0.12 ( syst ) ] % and Δ Y = [ 0.09 ± 0.26 ( stat ) ± 0.06 ( syst ) ] % , where Δ Y constrains possible C P violation. The y C P result excludes the null mixing hypothesis at 3.3 σ significance. This analysis is based on an integrated luminosity of 468     fb − 1 collected with the BABAR detector at the PEP-II asymmetric-energy e + e − collider.