We combine time-dependent multi-waveband flux and linear polarization observations with submilliarcsecond-scale polarimetric images at λ = 7 mm of the BL Lacertae type blazar OJ287 to locate the γ-ray emission in prominent flares in the jet of the source >14 pc from the central engine. We demonstrate a highly significant correlation between the strongest γ-ray and millimeter-wave flares through Monte Carlo simulations. The two reported γ-ray peaks occurred near the beginning of two major millimeter-wave outbursts, each of which is associated with a linear polarization maximum at millimeter wavelengths. Our very long baseline array observations indicate that the two millimeter-wave flares originated in the second of two features in the jet that are separated by >14 pc. The simultaneity of the peak of the higher-amplitude γ-ray flare and the maximum in polarization of the second jet feature implies that the γ-ray and millimeter-wave flares are cospatial and occur >14 pc from the central engine. We also associate two optical flares, accompanied by sharp polarization peaks, with the two γ-ray events. The multi-waveband behavior is most easily explained if the γ-rays arise from synchrotron self-Compton scattering of optical photons from the flares. We propose that flares are triggered by interaction of moving plasma blobs with a standing shock. The γ-ray and optical emission is quenched by inverse Compton losses as synchrotron photons from the newly shocked plasma cross the emission region. The millimeter-wave polarization is high at the onset of a flare, but decreases as the electrons emitting at these wavelengths penetrate less polarized regions.
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