We use Chandra observations to estimate the accretion rate of hot gas onto the central supermassive black hole in four giant (of stellar mass 10E11 - 10E12 solar masses) early-type galaxies located in the Virgo cluster. They are characterized by an extremely low radio luminosity, in the range L < 3E25 - 10E27 erg/s/Hz. We find that, accordingly, accretion in these objects occurs at an extremely low rate, 0.2 - 3.7 10E-3 solar masses per year, and that they smoothly extend the relation accretion - jet power found for more powerful radio-galaxies. This confirms the dominant role of hot gas and of the galactic coronae in powering radio-loud active galactic nuclei across ~ 4 orders of magnitude in luminosity. A suggestive trend between jet power and location within the cluster also emerges.