CERN-LHC. We present the first study of W+- W+- JET JET, 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+- MU+-, and MU+- MU+-) 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+- JET JET production and electroweak-only W+- W+- JET JET production is observed with a significance of 4.5 and 3.6 standard deviations respectively. The first region or "inclusive region" is defined to study the combination of electroweak and strong production mechanisms, and in this region both processes are referred to as signal. It is defined at particle level as follows. Exactly two prompt charged leptons (tau leptons and leptons originating from tau decays are excluded) are required with the same electric charge, transverse momentum PT > 25 GeV, ABS(ETA) < 2.5, invariant mass M > 20 GeV, and angular separation DELTA(R) = SQRT( DELTA(PHI)**2 + DELTA(ETA)**2 ) > 0.3. At least two jets reconstructed with the anti-kt algorithm with jet size R = 0.4 and with PT > 30 GeV, ABS(ETA) < 4.5, and separated from the leptons by DELTA(R(LEPTON JET)) > 0.3 are also required. The invariant mass of the two jets with the largest PT must be larger than 500 GeV, and the magnitude of the missing transverse momentum reconstructed using all neutrinos in the final state must be greater than 40 GeV. To reduce the dependence on QED radiation, lepton momenta include contributions from photons within DELTA(R) = 0.1 of the lepton direction. The second region or "VBS region" is a subset of the inclusive region that also requires the two jets with largest PT to be separated in rapidity by DELTA(Y(JET JET)) > 2.4. This enhances the purity of electroweak W+- W+- JET JET by removing most of the strong W+- W+- JET JET events, which are considered as a background in this region.