We present a study of the z = 2.07 quasar PKS 0528 + 134, which has been detected as an extraordinarily luminous gamma-ray source. Its radio properties are highly variable in both total and polarized flux density. Prior to mid-1991, the spectrum displayed a sharp peak at 5-8 GHz; since then, a major increase in nonthermal activity has caused the peak to move to approximately 60 GHz. The highest flux density at 37 GHz during this prolonged outburst occurred within two weeks of the brightest gamma-ray flux yet measured. Milliarcsecond-scale maps from global VLBI experiments, an X-ray spectrum from ROSAT PSPC observations, and light curves in total flux density and polarization are used to investigate the geometry, radiation mechanism, and physical environment of the emission region in the source. The VLBI images reveal a bent jet extending toward the northeast on parsec scales, with less intense knots of emission appearing on the opposite side of the brightest spot. The position of the core usually found in such sources is unclear. The polarization position angle is stable despite strong variability in polarized flux density and indicates that the magnetic field is aligned with the jet axis as defined by our 8.4 GHz image. The ROSA T X-ray flux density of PKS 0528 + 134 in 1991 March is measured to be 1.6 muJy at 1 keV, with a very steep spectral ('' energy '') index sigma(x) almost-equal-to 2.2. The X-ray observations reveal the presence of cold gas along the line of sight significantly in excess of that present in the Galaxy. A strong radio flare began within two months of the first observation of a high flux of gamma-rays from PKS 0528 + 134 by Hunter et al. Using the geometry and spectral characteristics determined by our VLBI observations, a synchrotron self-Compton calculation indicates that relativistic bulk motion is required in PKS 0528 + 134, with an estimated Doppler beaming factor delta greater than or equal to 4.3, similar to the value delta greater than or equal to 7 required to explain the low optical depth of the gamma-rays to photon-photon pair production. We suggest that the core activity of PKS 0528+134 is sporadic in nature, with the nonthermal outburst starting in 1991 representing a violent period involving ejection of relativistic plasma along a compact jet pointed almost directly toward us. The quasar may be in the process of evolving from a GHz-peaked spectrum (GPS) source into a core-jet source. The nature of the apparent counterjet and the location of the true core of the source can only be determined by further VLBI observations.
