  We present the results of a 400ks Chandra survey of 29 extended Ly-alpha
emitting nebulae (Ly-alpha Blobs, LABs) in the z=3.09 proto-cluster in the
SSA22 field. We detect luminous X-ray counterparts in five LABs, implying a
large fraction of active galactic nuclei (AGN) in LABs, f_AGN = 17% down to
L_2-32keV ~ 10^44 erg/s. 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 >9Ms 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>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.
