An inclusive search for anomalous production of two prompt, isolated leptons with the same electric charge is presented. The search is performed in a data sample corresponding to 4.7 fb(-1) of integrated luminosity collected in 2011 at root s = 7TeV with the ATLAS detector at the LHC. Pairs of leptons (e(+/-)e(+/-), e(+/-)mu(+/-), and mu(+/-)mu(+/-)) with large transverse momentum are selected, and the dilepton invariant mass distribution is examined for any deviation from the Standard Model expectation. No excess is found, and upper limits on the production cross section of like-sign lepton pairs from physics processes beyond the Standard Model are placed as a function of the dilepton invariant mass within a fiducial region close to the experimental selection criteria. The 95% confidence level upper limits on the cross section of anomalous e(+/-)e(+/-), e(+/-)mu(+/-), or mu(+/-)mu(+/-) production range between 1.7 fb and 64 fb depending on the dilepton mass and flavour combination.