We present the first systematic 1.4 GHz Very Large Array radio continuum survey of fossil galaxy group candidates. These are virialized systems believed to have assembled over a gigayear in the past through the merging of galaxy group members into a single, isolated, massive elliptical galaxy and featuring an extended hot X-ray halo. We use new photometric and spectroscopic data from SDSS Data Release 7 to determine that three of the candidates are clearly not fossil groups. Of the remaining 30 candidates, 67% contain a radio-loud (L_1.4GHz > 10^23 W Hz^-1) active galactic nucleus (AGN) at the center of their dominant elliptical galaxy. We find a weak correlation between the radio luminosity of the AGN and the X-ray luminosity of the halo suggesting that the AGN contributes to energy deposition into the intragroup medium. We only find a correlation between the radio and optical luminosity of the central elliptical galaxy when we include X-ray selected, elliptically dominated non-fossil groups, indicating a weak relationship between AGN strength and the mass assembly history of the groups. The dominant elliptical galaxy of fossil groups is on average roughly an order of magnitude more luminous than normal group elliptical galaxies in optical, X-ray, and radio luminosities and our findings are consistent with previous results that the radio-loud fraction in elliptical galaxies is linked to the stellar mass of a population. The current level of activity in fossil groups suggests that AGN fueling continues long after the last major merger. We discuss several possibilities for fueling the AGN at the present epoch.
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