Recent high-energy gamma-ray observations (E(gamma) > 100 MeV) of blazar AGNs show emission spectra with no clear upper energy cutoff. AGNs, considered to be possible sources for the observed flux of cosmic rays beyond 10(19) eV, may well have emission extending into the VHE (very high energy, E(gamma) > 100 GeV) domain. Because VHE gamma-rays are absorbed by pair production on the intergalactic background radiation fields, much of this emission may not be directly visible. The electromagnetic cascades initiated by absorbed VHE gamma-rays, however, may be observable. Since, most probably, the velocities of (e+, e-) pairs produced in a cascade are quickly isotropized by an ambient random magnetic field, extended '' halos '' (R > 1 Mpc) of pairs will be formed around AGNs with VHE emission. The cascade radiation from these pair halos is emitted isotropically and should be observable at energies below a few TeV. The halo radiation can be distinguished by its characteristic variation in spectrum and intensity with angular distance from the central source. This variation depends weakly on the details of the central source model, e.g., the orientation and beaming/opening angle of an emitting jet. Limiting or determining the intensity of the pair halo can thus serve as a model-independent bound on or measure of the VHE power of AGNs. Next-generation Cherenkov telescopes may be able to image a pair halo.