This Letter presents a search for contact interactions in the dielectron and dimuon channels using data from proton–proton collisions produced by the LHC at √s = 7 TeV and recorded by the ATLAS detector. The data sample, collected in 2011, corresponds to an integrated luminosity of 1.08 and 1.21 fb−1 in the e+e− and μ+μ− channels, respectively. No significant deviations from the standard model are observed. Using a Bayesian approach with a prior flat in 1/Λ2, the following 95% CL lower limits are placed on the energy scale of contact interactions: Λ− > 10.1 TeV (Λ+ > 9.4 TeV) in the electron channel and Λ− > 8.0 TeV (Λ+ > 7.0 TeV) in the muon channel for constructive (destructive) interference in the left–left isoscalar contact interaction model. Limits are also provided for a prior flat in 1/Λ4.