In high-energy heavy-ion collisions, the correlations between the emitted particles can be used as a probe to gain insight into the charge creation mechanisms. In this article, we report the first results of such studies using the electric charge balance function in the relative pseudorapidity \Delta\eta and azimuthal angle \Delta\phi in Pb-Pb collisions at sqrt{s_{NN}} = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The width of the balance function decreases with growing centrality (i.e. for more central collisions) in both projections. This centrality dependence is not reproduced by HIJING, while AMPT, a model which incorporates strings and parton rescattering, exhibits qualitative agreement with the measured correlations in \Delta\phi but fails to describe the correlations in \Delta\eta. A thermal blast wave model incorporating local charge conservation and tuned to describe the p_T spectra and v_2 measurements reported by ALICE, is used to fit the centrality dependence of the width of th