A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb-1 of sqrt(s) = 7 TeV proton-proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results.