  We have made a 30 ksec Chandra observation of the redshift z=0.63 GPS quasar
B2 0738+313. We detected X-ray emission from the core and have discovered a 200
kpc (projected on the sky) X-ray jet. The X-ray jet is narrow and curves,
following the extended radio structure to the south of the quasar, and ending
with a hot spot at the southernmost part of the radio lobe. The jet has a knot
at ~13 arcsec away from the core. The knot emission is consistent with the
X-rays being created by the inverse Compton scattering of the cosmic microwave
background (CMB) photons and requires jet bulk Lorentz factors of a few
(Gamma_{bulk} ~ 5-7). We discuss the emission mechanisms that may be
responsible for the jet emission. We present new VLA data of the core and jet,
and discuss the relation between the extended radio and X-ray emission.
Extended emission observed in several GPS sources has been interpreted as a
signature of the source past activity, while the GPS source is young and newly
expanded. We argue that B2~0738+313 may be an example of a new class of radio
sources similar to the FRII radio galaxies in their high jet bulk velocities,
but with the powerful GPS-like nucleus.
  B2 0738+313 also has two damped Lyman-alpha systems along the line of sight,
at z_{abs} = 0.0912 and 0.2212. We discuss the possible connection between the
X-ray absorption (7.2+/-0.9 e20 cm(-2)) detected in the ACIS spectrum and these
two intervening absorbers. We also investigate an extended structure within the
central 10 arcsec of the core in the relation to structure seen in the optical.
