Aims. We present an analysis of the 700 ks Chandra ACIS-S observation of the field around the radio galaxy J1140-2629 (the Spiderweb Galaxy) at z = 2:156, focusing on the nuclear activity in the associated large-scale environment. Methods. We identified unresolved X-ray sources in the field down to flux limits of 1:3 × 10-16 and 3:9 × 10-16 erg s-1 cm in the soft (0.5 2.0 keV) and hard (2 10 keV) band, respectively. We searched for counterparts in the optical, near-infrared, and submillimeter catalogs available in the literature to identify X-ray sources belonging to the protocluster and derived their X-ray properties. Results. We detect 107 X-ray unresolved sources within 5 arcmin (corresponding to 2.5 Mpc) of J1140-2629, among which 13 have optical counterparts with spectroscopic redshift 2:11 < z < 2:20, and 1 source has a photometric redshift consistent with this range. The X-ray-emitting protocluster members are distributed approximately over a ∼3:2 × 1:3 Mpc2 rectangular region. An X-ray spectral analysis for all the sources within the protocluster shows that their intrinsic spectral slope is consistent with an average hGi ∼ 1:84 ± 0:04. Excluding the Spiderweb Galaxy, the best-fit intrinsic absorption for five protocluster X-ray members is NH > 1023 cm-2, while another six have upper limits of the order of a few times 1022 cm-2. Two sources can only be fitted with very flat G = 1, and are therefore considered Compton-thick candidates. The 0.5 10 keV rest-frame luminosities of the 11 Compton-thin protocluster members corrected for intrinsic absorption are greater than 2 × 1043 erg s-1. These values are typical for the bright end of a Seyfert-like distribution and significantly greater than X-ray luminosities expected from star formation activity. The X-ray luminosity function of the AGN in the volume associated to the Spiderweb protocluster in the range 1043 < LX < 1044:5 erg s-1 is at least ten times higher than that in the field at the same redshift and significantly flatter, implying an increasing excess at the bright end. The X-ray AGN fraction is measured to be 25:5 ± 4:5% of the spectroscopically confirmed members in the stellar mass range log(M*=M) > 10:5. This value corresponds to an enhancement factor of 6:0+9:0-3:0 for the nuclear activity with L0:5-10 keV > 4 × 1043 erg s-1 with respect to the COSMOS field at comparable redshifts and stellar mass range. Conclusions. We conclude that the galaxy population in the Spiderweb protocluster is characterized by enhanced X-ray nuclear activity triggered by environmental effects on megaparsec scales.