We present a measurement of D 0 − ¯¯¯ D 0 mixing parameters using the ratios of lifetimes extracted from a sample of D 0 mesons produced through the process D * + → D 0 π + , which decay to K − π + , K − K + , or π − π + . The lifetimes of the C P -even, Cabibbo-suppressed modes K − K + and π − π + are compared with that of the C P -mixed, Cabibbo-favored mode K − π + to obtain a measurement of y C P , which in the limit of C P conservation corresponds to the mixing parameter y . The analysis is based on a data sample of 384     fb − 1 collected by the BABAR detector at the PEP-II asymmetric-energy e + e − collider. We obtain y C P = [ 1.24 ± 0.39 ( stat ) ± 0.13 ( syst ) ] % , which is evidence for D 0 − ¯¯¯ D 0 mixing at the 3 σ level, and Δ Y = [ − 0.26 ± 0.36 ( stat ) ± 0.08 ( syst ) ] % , where Δ Y constrains possible C P violation. Combining this result with a previous BABAR measurement of y C P obtained from a separate sample of D 0 → K − K + events, we obtain y C P = [ 1.03 ± 0.33 ( stat ) ± 0.19 ( syst ) ] % .