An 11 day monitoring campaign in late 2005 reveals clear correlation in polarization between the optical emission and the region of the intensity peak (the "pseudocore") at the upstream end of the jet in 43 GHz VLBA (Very Long Baseline Array) images in the highly variable quasar PKS 0420-014. The electric-vector position angle (EVPA) of the pseudocore rotated by about 80° in four VLBA observations over a period of 9 days, matching the trend of the optical EVPA. In addition, the 43 GHz EVPAs agree well with the optical values when we correct the former for Faraday rotation. Fluctuations in the polarization at both wave bands are consistent with the variable emission arising from a standing conical shock wave that compresses magnetically turbulent plasma in the ambient jet. The volume of the variable component is the same at both wave bands, although only ∼20% of the total 43 GHz emission arises from this site. The remainder of the 43 GHz flux density must originate in a separate region with very low polarization. If 0420-014 is a typical case, the nonthermal optical emission from blazars originates primarily in and near the pseudocore rather than closer to the central engine where the flow collimates and accelerates.