We present the results of a 400 ks Chandra survey of 29 extended Ly \alpha emitting nebulae ( Ly \alpha Blobs , LABs ) in the z = 3.09 proto-cluster in the SS A22 field . We detect luminous X-ray counterparts in five LABs , implying a large fraction of active galactic nuclei ( AGN ) in LABs , f _ { AGN } = 17 ^ { +12 } _ { -7 } % down to L _ { 2 - 32 keV } \sim 10 ^ { 44 } erg s ^ { -1 } . All of the AGN appear to be heavily obscured , with spectral indices implying obscuring column densities of N _ { H } > 10 ^ { 23 } cm ^ { -2 } . The AGN fraction should be considered a lower limit , since several more LABs not detected with Chandra show AGN signatures in their mid-infrared emission . We show that the UV luminosities of the AGN are easily capable of powering the extended Ly \alpha emission via photo-ionization alone . When combined with the UV flux from a starburst component , and energy deposited by mechanical feedback , we demonstrate that ‘ heating ’ by a central source , rather than gravitational cooling is the most likely power source of LABs . We argue that all LABs could be powered in this manner , but that the luminous host galaxies are often just below the sensitivity limits of current instrumentation , or are heavily obscured . No individual LABs show evidence for extended X-ray emission , and a stack equivalent to a \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 9 Ms exposure of an average LAB also yields no statistical detection of a diffuse X-ray component . The resulting diffuse X-ray/Ly \alpha luminosity limit implies there is no hot ( T \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 10 ^ { 7 } K ) gas component in these halos , and also rules out inverse Compton scattering of cosmic microwave background photons , or local far-infrared photons , as a viable power source for LABs .