A measurement of the top-antitop ($t\bar{t}$) charge asymmetry is presented using data corresponding to an integrated luminosity of 4.6 fb$^{-1}$ of LHC $pp$ collisions at a centre-of-mass energy of 7 TeV collected by the ATLAS detector. Events with two charged leptons, at least two jets and large missing transverse momentum are selected. Two observables are studied: $A^{\ell\ell}_{\textrm{C}}$ based on the identified charged leptons, and $A^{t\bar{t}}_{\textrm{C}}$, based on the reconstructed $t\bar{t}$ final state. The asymmetries are measured to be \begin{eqnarray*} A^{\ell\ell}_{\textrm{C}} & = & 0.024 \pm 0.015 ~\textrm{(stat.)} \pm 0.009 ~\textrm{(syst.)}, \end{eqnarray*} \begin{eqnarray*} A^{t\bar{t}}_{\textrm{C}} & = & 0.021 \pm 0.025 ~\textrm{(stat.)} \pm 0.017 ~\textrm{(syst.)}. \end{eqnarray*} The measured values are in agreement with the Standard Model
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