The first measurement of e+e− pair production at mid-rapidity (|ηe| < 0.8) in pp collisions at √s=7 TeV with ALICE at the LHC is presented. The dielectron production is studied as a function of the invariant mass (mee < 3.3 GeV/c2), the pair transverse momentum (pT,ee < 8 GeV/c), and the pair transverse impact parameter (DCAee), i.e., the average distance of closest approach of the reconstructed electron and positron tracks to the collision vertex, normalised to its resolution. The results are compared with the expectations from a cocktail of known hadronic sources and are well described when PYTHIA is used to generate the heavy-flavour contributions. In the low-mass region (0.14 < mee < 1.1 GeV/c2), prompt and non-prompt e+e− sources can b...