A study of indirect C P violation in D 0 mesons through the determination of the parameter A Γ is presented using a data sample of p p collisions, corresponding to an integrated luminosity of 1.0     fb − 1 , collected with the LHCb detector and recorded at the center-of-mass energy of 7 TeV at the LHC. The parameter A Γ is the asymmetry of the effective lifetimes measured in decays of D 0 and ¯ D 0 mesons to the C P eigenstates K − K + and π − π + . Fits to the data sample yield A Γ ( K K ) = ( − 0.35 ± 0.62 ± 0.12 ) × 10 − 3 and A Γ ( π π ) = ( 0.33 ± 1.06 ± 0.14 ) × 10 − 3 , where the first uncertainties are statistical and the second systematic. The results represent the world's best measurements of these quantities. They show no difference in A Γ between the two final states and no indication of C P violation.