  NGC 4477 is a low-mass lenticular galaxy in the Virgo Cluster, residing at
100\,kpc to the north of M87. Using a total of 116\,ks {\sl Chandra}
observations, we study the interplay between its hot ($\sim$0.3\,keV) gas halo
and the central supermassive black hole. A possible cool core is indicated by
the short cooling time of the gas at the galaxy centre. We identify a pair of
symmetric cavities lying 1.1\,kpc southeast and 0.9\,kpc northwest of the
galaxy centre with diameters of 1.3\,kpc and 0.9\,kpc, respectively. We
estimate that these cavities are newly formed with an age of $\sim$4\,Myr. No
radio emission is detected at the positions of the cavities with the existing
VLA data. The total energy required to produce the two cavities is
$\sim$$10^{54}$\,erg, at least two orders of magnitude smaller than that of
typical X-ray cavities. NGC 4477 is arguably far the smallest system and the
only lenticular galaxy in which AGN X-ray cavities have been found. It falls on
the scaling relation between the cavity power and the AGN radio luminosity,
calibrated for groups and clusters. Our findings suggest that AGN feedback is
universal among all cool core systems. Finally, we note the presence of
molecular gas in NGC~4477 in the shape of a regular disk with ordered rotation,
which may not be related to the feedback loop.
