  Indirect CP violation in the $D^0$ system can be probed by measuring the
parameter $A_{\Gamma}$, defined as the CP asymmetry of the effective lifetime
of the $D^0$ meson decaying to a CP eigenstate. This can be significantly
enhanced beyond Standard Model predictions by new physics. Measurements of
$A_{\Gamma}$ using $D^0 \rightarrow K^+K^-$ and $D^0\rightarrow \pi^+\pi^-$
decays reconstructed from pp collisions collected by the LHCb experiment,
corresponding to an integrated luminosity of 1.0 fb$^{-1}$, are presented. The
results are \begin{align*}
  A_{\Gamma} (\pi\pi) = (+0.33 \pm 1.06 \pm 0.14) \times 10^{-3},\quad
  A_{\Gamma} (KK) = (-0.35 \pm 0.62 \pm 0.12) \times 10^{-3}, \end{align*}
where the uncertainties are statistical and systematic, respectively. These are
the most precise measurements of their kind to date, and show no evidence of CP
violation.
