  We report the discovery of a faint optical tidal disruption event (TDE) in
the nearby star-forming galaxy NGC 3799. Identification of the TDE is based on
its position at the galaxy nucleus, a light curve declining as t^-5/3, a blue
continuum with an almost constant blackbody temperature of ~12,000K, and broad
(~15,000kms^-1) Balmer lines and characteristic He~II 4686A emission. The light
curve of AT 2023clx peaked at an absolute magnitude of -17.16mag in the g-band
and a maximum blackbody bolometric luminosity of 4.56*10^42 ergs^-1, making it
the faintest TDE discovered to date. With a redshift of 0.01107 and a
corresponding luminosity distance of 47.8Mpc, it is also the closest optical
TDE ever discovered to our best knowledge. Furthermore, our analysis of
Swift/XRT observations of AT 2023clx yields a very tight 3 sigma upper limit of
9.53*10^39 ergs^-1 in the range 0.3--10keV. AT 2023clx, together with very few
other faint TDEs such as AT 2020wey, prove that there are probably a large
number of faint TDEs yet to be discovered at higher redshifts, which is
consistent with the prediction of luminosity functions (LFs). The upcoming
deeper optical time-domain surveys, such as the Legacy Survey of Space and Time
(LSST) and the Wide-Field Survey Telescope (WFST) will discover more TDEs at
even lower luminosities, allowing for a more precise constraint of the low-end
of the LF.
