  We present the discovery of the fading radio transient FIRST
J153350.8+272729. The source had a maximum observed 5-GHz radio luminosity of
$8\times10^{39}$ erg s$^{-1}$ in 1986, but by 2019 had faded by a factor of
nearly 400. It is located 0.15 arcsec from the center of a galaxy (SDSS
J153350.89+272729) at 147 Mpc, which shows weak Type II Seyfert activity. We
show that a tidal disruption event (TDE) is the preferred scenario for FIRST
J153350.8+272729, although it could plausibly be interpreted as the afterglow
of a long-duration gamma-ray burst. This is only the second TDE candidate to be
first discovered at radio wavelengths. Its luminosity fills a gap between the
radio afterglows of sub-relativistic TDEs in the local universe, and
relativistic TDEs at high redshifts. The unusual properties of FIRST
J153350.8+272729 (ongoing nuclear activity in the host galaxy, high radio
luminosity) motivate more extensive TDE searches in untargeted radio surveys.
