We analyze the linear polarization of the relativistic jet in BL Lacertae object OJ~287 as revealed by multi-epoch Very Long Baseline Array (VLBA) images at 43 GHz and monitoring observations at optical bands. The electric-vector position angle (EVPA) of the optical polarization matches that at 43 GHz at locations that are often in the compact millimeter-wave core or, at other epochs, coincident with a bright, quasi-stationary emission feature $sim0.2$~milliarcsec ($sim$0.9~pc projected on the sky) downstream from the core. This implies that electrons with high enough energies to emit optical synchrotron and $gamma$-ray inverse Compton radiation are accelerated both in the core and at the downstream feature, the latter of which lies $geq10$~pc from the central engine. The polarization vector in the stationary feature is nearly parallel to the jet axis, as expected for a conical standing shock capable of accelerating electrons to GeV energies.
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