A recent Chandra observation of the nearby galaxy cluster Abell 585 has led to the discovery of an extended X-ray jet associated with the high-redshift background quasar B3 0727+409, a luminous radio source at redshift z = 2.5. This is one of only few examples of high-redshift X-ray jets known to date. It has a clear extension of about 12'', corresponding to a projected length of ~100 kpc, with a possible hot spot located 35'' from the quasar. The archival high resolution Very Large Array maps surprisingly reveal no extended jet emission, except for one knot about 1_{.}^{"}\textrm{4} from the quasar. The high X-ray to radio luminosity ratio for this source appears consistent with the ∝ \left ( 1+z \right )^{4} amplification expected from the inverse Compton radiative model. This serendipitous discovery may signal the existence of an entire population of similar systems with bright X-ray and faint radio jets at high redshift, a selection bias that must be accounted for when drawing any conclusions about the redshift evolution of jet properties and indeed about the cosmological evolution of supermassive black holes and active galactic nuclei in general.