Since the discovery of kiloparsec-scale X-ray emission from quasar jets, the physical processes responsible for their high-energy emission have been poorly defined. A number of mechanisms are under active debate, including synchrotron radiation, inverse-Comptonized CMB (IC/CMB) emission, and other Comptonization processes. In a number of cases, the optical and X-ray emission of jet regions are inked by a single spectral component, and in those, high- resolution multi-band imaging and polarimetry can be combined to yield a powerful diagnostic of jet emission processes. Here we report on deep imaging photometry of the jet of PKS 1136$-$135 obtained with the {it Hubble Space Telescope.} We find that several knots are highly polarized in the optical, with fractional polarization $Pi>30%$. When combined with the broadband spectral shape observed in these regions, this is very difficult to explain via IC/CMB models, unless the scattering particles are at the lowest-energy tip of the electron energy distribution, with Lorentz factor $gamma sim 1$, and the jet is also very highly beamed ($delta geq 20$) and viewed within a few degrees of the line of sight. We discuss both the IC/CMB and synchrotron interpretation of the X-ray emission in the light of this new evidence, presenting new models of the spectral energy distribution and also the matter content of this jet. The high polarizations do not completely rule out the possibility of IC/CMB optical-to-X-ray emission in this jet, but they do strongly disfavor the model. We discuss the implications of this finding, and also the prospects for future work.
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