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This Letter presents the first study of $W^{\pm}W^{\pm}jj$,same-electric-charge diboson production in association with two jets, using20.3 fb$^{-1}$ of proton--proton collision data at $\sqrt{s}=8$ TeV recorded bythe ATLAS detector at the Large Hadron Collider. Events with two reconstructedsame-charge leptons ($e^\pm e^\pm$, $e^\pm \mu^\pm$, and $\mu^\pm \mu^\pm$) andtwo or more jets are analyzed. Production cross sections are measured in twofiducial regions, with different sensitivities to the electroweak and strongproduction mechanisms. First evidence for $W^{\pm}W^{\pm}jj$ production andelectroweak-only $W^{\pm}W^{\pm}jj$ production is observed with a significanceof $4.5$ and $3.6$ standard deviations respectively. The measured productioncross sections are in agreement with Standard Model predictions. Limits at 95%confidence level are set on anomalous quartic gauge couplings.

Evidence for Electroweak Production of $W^{\pm}W^{\pm}jj$ in $pp$ Collisions at $\sqrt{s}=8$ TeV with the ATLAS Detector