This Letter presents the first study of W(±)W(±)jj, same-electric-charge diboson production in association with two jets, using 20.3 fb(-1) of proton-proton collision data at sqrt[s] = 8 TeV recorded by the ATLAS detector at the Large Hadron Collider. Events with two reconstructed same-charge leptons (e(±)e(±), e(±)μ(±), and μ(±)μ(±)) and two or more jets are analyzed. Production cross sections are measured in two fiducial regions, with different sensitivities to the electroweak and strong production mechanisms. First evidence for W(±)W(±)jj production and electroweak-only W(±)W(±)jj production is observed with a significance of 4.5 and 3.6 standard deviations, respectively. The measured production cross sections are in agreement with standard model predictions. Limits at 95% confidence level are set on anomalous quartic gauge couplings.