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 √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.