We present evidence for a highly obscured X-ray source in one of two giant Ly-alpha emission nebulae in the z=3.09 proto-cluster region SSA22. Neither Ly-alpha nebula is associated with significant radio emission. While one has a significant submillimeter detection and is undetected in the X-ray, the other is a factor of 2-10 times less submillimeter bright and appears to contain a hard-band X-ray source. We discuss our analysis and techniques for assessing the X-ray properties of this source and suggest that we have detected an embedded AGN source in one of these nebulae which may be at least partially responsible for exciting the Ly-alpha emission through a mechanism that is essentially decoupled from the radio, submillimeter, or optical luminosities. We also present an upper limit on the mean X-ray emission from 10 other extended Ly-alpha objects in the SSA22 region.