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 PKSÂ 1136 - 135 obtained with the 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 .