X-ray jets in AGN are commonly observed in FRII and FRI radio-galaxies, but rarely in BL Lacs, most probably due to their orientation close to the line of sight and the ensuing foreshortening effects. Only three BL Lacs are known so far to contain a kpc-scale X-ray jet. In this paper, we present the evidence for the existence of a fourth extended X-ray jet in the classical radio-selected source S5 2007+777, which for its hybrid FRI/II radio morphology has been classified as a HYMOR (HYbrid MOrphology Radio source). Our Chandra ACIS-S observations of this source revealed an X-ray counterpart to the 19-long radio jet. Interestingly, the X-ray properties of the kpc-scale jet in S5 2007+777 are very similar to those observed in FRII jets. First, the X-ray morphology closely mirrors the radio one, with the X-rays being concentrated in the discrete radio knots. Second, the X-ray continuum of the jet/brightest knot is described by a very hard power law, with photon index Gamma_x~1, although the uncertainties are large. Third, the optical upper limit from archival HST data implies a concave radio-to-X-ray SED. If the X-ray emission is attributed to IC/CMB with equipartition, strong beaming (delta=13) is required, implying a very large scale (Mpc) jet. The beaming requirement can be somewhat relaxed assuming a magnetic field lower than equipartition. Alternatively, synchrotron emission from a second population of very high-energy electrons is viable. Comparison to other HYMOR jets detected with Chandra is discussed, as well as general implications for the origin of the FRI/II division.