  We present the X-ray imaging and spectral analysis of the diffuse emission
around the Spiderweb galaxy at z=2.16 and of its nuclear emission, based on a
deep (700 ks) Chandra observation. We characterize the nuclear emission and
computed the contamination in the surrounding regions due to the wings of the
instrument PSF. Then, we quantified the extended emission within 12". We find
that the Spiderweb galaxy hosts a mildly absorbed quasar, with modest yet
significant variability on a timescale of ~1 year. We find that the emission in
the jet regions is well described by a power law with Gamma~2-2.5, and it is
consistent with IC upscattering of the CMB photons by the relativistic
electrons. We also find a roughly symmetric, diffuse emission within a radius
of ~100 kpc. This emission is consistent with thermal bremsstrahlung from a hot
ICM with a temperature of kT=2.0_{-0.4}^{+0.7} keV, and a metallicity of
Z<1.6Z_sun. The average electron density within 100 kpc is
n_e=(1.51+-0.24+-0.14)E-2 cm^{-3}, corresponding to an upper limit for the
total ICM mass of <=(1.76+-0.30+-0.17)E+12 M_sun (where error bars are 1 sigma
statistical and systematic, respectively). If we apply hydrostatic equilibrium
to the ICM, we measure a total gravitational mass M(<100
kpc)=(1.5^{+0.5}_{-0.3})E+13 M_sun and, extrapolating at larger radii, we
estimate a total mass M_{500}=(3.2^{+1.1}_{-0.6})E+13 M_sun within a radius of
r_{500}=(220+-30) kpc. We conclude that the Spiderweb protocluster shows
significant diffuse emission within a radius of 12 arcsec, whose major
contribution is provided by IC scattering associated with the radio jets.
Outside the jet regions, we also identified thermal emission within a radius of
~100 kpc, revealing the presence of hot, diffuse baryons that may represent the
embryonic virialized halo of the forming cluster.
