Using Chandra imaging spectroscopy and Very Large Array L-band maps, we have identified radio galaxies at P (1.4 GHz) 3 × 10 23 W Hz −1 and X-ray point sources (XPSs) at L (0.3-8 keV) 10 42 erg s −1 in 11 moderate redshift (0.2 < z < 0.4) clusters of galaxies. Each cluster is uniquely chosen to have a total mass similar to predicted progenitors of the present-day Coma Cluster. Within a projected radius of 1 Mpc we detect 20 radio galaxies and 8 XPSs (three sources are detected in both X-ray and radio) confirmed to be cluster members above these limits. Of these, 75% are detected within 500 kpc (projected) of the cluster center. This result is inconsistent with a random selection from bright, red sequence ellipticals at the >99.999% level. We suggest that these active galactic nuclei (AGNs) are triggered somehow by the intracluster medium (ICM), perhaps similar to the Bondi accretion model of Allen et al. All but one of the XPSs are hosted by luminous ellipticals which otherwise show no other evidence for AGN activity. These objects are unlikely to be highly obscured AGN since there is no evidence for large amounts of X-ray or optical absorption. One XPS, in addition to possessing a pure absorption-line optical spectrum, has a large excess of light blueward of the Ca ii H&K break that could be nonthermal emission; a second XPS host galaxy probably has excess blue light. The most viable model for these sources are low-luminosity BL Lac Objects, similar to the high-energy-peaked BL Lacs (HBLs) discovered in abundance in serendipitous X-ray surveys. The expected numbers of lower luminosity FR 1 radio galaxies and HBLs in our sample converge to suggest that very deep radio and X-ray images of rich clusters will detect AGN (either X-ray or radio emitting or both) in a large fraction of bright elliptical galaxies in the inner 500 kpc. Because both the radio galaxies and the XPSs possess relativistic jets, they (and, by extension, the entire radio luminosity function) can inject heat into the ICM. Using the most recent scalings of P jet ∝ L 0.5 r from Bîrzan et al., radio sources weaker than our luminosity limit probably contribute the majority of the heat to the ICM. Also, because these heat sources move around the cluster, AGN heating is distributed rather evenly. If a majority of ICM heating is due to large numbers of low-power radio sources, triggered into activity by the increasing ICM density as they move inward, this may be the feedback mechanism necessary to stabilize cooling in cluster cores.