  We report the Chandra detection of an X-ray jet in 3C 15. The peak of the
X-ray emission in the jet is 4.1'' (a projected distance of 5.1 kpc) from the
nucleus, and coincident with a component previously identified in the radio and
optical jets. We examine four models for the X-ray jet emission: (I) weak
synchrotron cooling in equip., (II) moderate synchrotron cooling in equip.,
(III) weak synchrotron plus SSC cooling, and (IV) moderate synchrotron plus SSC
cooling. We argue that case (II) can most reasonably explain the overall
emission from knot C. Case (III) is also possible, but requires a large
departure from equipartition and for the jet power to be comparable to that of
the brightest quasars. Diffuse X-ray emission has also been detected,
distributed widely over the full extent (63kpc x 25kpc) of the radio lobes. We
compare the total energy contained in the lobes with the jet power estimated
from knot C, and discuss the energetic link between the jet and the lobes. We
argue that the fueling time (t_fuel) and the source age (t_src) are comparable
for case (II), whereas t_fuel << t_src is likely for case (III). The latter may
imply that the jet has a very small filling factor, ~10^{-3}. We consider the
pressure balance between the thermal galaxy halo and non-thermal relativistic
electrons in the radio lobes. Finally, we show that the X-ray emission from the
nucleus is not adequately fitted by a simple absorbed power-law model, but
needs an additional power-law with heavy absorption intrinsic to the source.
Such a high column density is consistent with the presence of a dense, dusty
torus which obscures the quasar nucleus.
