A search for the electroweak production of gauginos decaying into two leptons and missing transverse momentum, [special characters omitted], is presented using pp collisions at [special characters omitted] = 7 TeV produced by the LHC and recorded by the ATLAS detector corresponding to an integrated luminosity of 4.7 fb⁻¹. Standard Model backgrounds are estimated using a combination of semi-data-driven techniques where possible, and Monte Carlo simulation. No significant excess in data with respect to the Standard Model prediction is observed in any of the four signal regions: opposite-sign dileptons with a jet veto and [special characters omitted], same-sign dileptons with a jet veto and [special characters omitted], opposite-sign dileptons in association with jets, or a signal region requiring opposite sign dileptons and using kinematic properties of the event to remove tt¯ and WW backgrounds. In addition to model-independent limits, limits are set in both simplified models and in the context of the phenomenological Minimally Supersymmetric Standard Model. Using the simplified model paradigm, wino-based charginos, decaying through an intermediate on-shell slepton or sneutrino to a stable 10 GeV neutralino, are excluded for chargino masses between 110 and 340 GeV. For the case of associatively produced mass-degenerate charginos and neutralinos both decaying via on-shell sleptons or sneutrinos to stable 10 GeV neutralinos, the chargino and neutralino masses of 80-260 GeV are excluded.