Recent rotation-measure observations of a dozen or so galaxyclusters have revealed a surprisingly large number of magnetic fields whose estimated energy and flux are, on average, ~ 1058 ergs and ~ 1041 G cm2, respectively. These quantities are so much larger than any coherent sums of individual galaxies within the cluster that an efficient galactic dynamo is required. We associate these fields with single AGNs within the cluster and, therefore, with all galaxies during their AGN phase. Only the central, massive black hole (BH) has the necessary binding energy, ~ 1061 ergs. Only the accretion disk during the BH formation has the winding number, ~ 1011 turns, necessary to make the gain and magnetic flux. We present a model of a BH accretion-disk dynamo that might create these magnetic fields, where the helicity of the α-Ω dynamo is driven by star-disk collisions. The back reaction of the saturated dynamo forms a force-free field helix that carries the energy and flux of the dynamo and redistributes them within the clusters.