We report a measurement of the CP violating asymmetry in D0 → π+π− decays using approximately 215,000 decays reconstructed in about 5.94 fb−1 of CDF data. We use the strong D*+ → D0π+ decay ("D* tag") to identify the flavor of the charmed meson at production time and exploit CP-conserving strong c pair-production in p collisions. Higher statistic samples of Cabibbo-favored D0 → K−π+ decays with and without D* tag are used to highly suppress systematic uncertainties due to detector effects. The result is the world's most precise measurement to date and it is fully consistent with no CP violation.