Faraday rotation measurements of the luminous radio galaxies 3C295, Cygnus A, and Hydra A, all of which are associated with cD galaxies located in massive cooling flow clusters, show very high rotation measures – typically a few thousand radm−2, exceeding 20,000 radm−2 for 3C295. The RMs vary over large ranges and with different scales. The RMs are both positive and negative, implying reversals of the magnetic field – the variations cannot be due to density changes alone. The RMs originate in magnetized cluster gas, but it is unclear what fraction is due to a coccoon surrounding the radio source. If from the cluster as a whole, the magnetic field is , where N is the number of cells along the line of sight. A good case can be made for an enhanced magnetic field localized at or near the surface of the radio source, accounting for a significant fraction of the observed RM.