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 & SIM;12,000 K, broad (& AP;15,000 km s(-1)) Balmer lines, and characteristic He ii 4686 & ANGS; emission. The light curve of AT 2023clx peaked at an absolute magnitude of -17.16 mag in the g band and a maximum blackbody bolometric luminosity of 4.56 x 10(42) erg s(-1), making it the faintest TDE discovered to date. With a redshift of 0.01107 and a corresponding luminosity distance of 47.8 Mpc, it is also the closest optical TDE ever discovered to the best of our knowledge. Furthermore, our analysis of Swift/XRT observations of AT 2023clx yields a very tight 3 & sigma; upper limit of 9.53 x 10(39) erg s(-1) in the range 0.3-10 keV. 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 and the Wide Field Survey Telescope, will discover more TDEs at even lower luminosities, allowing for a more precise constraint of the low end of the LF.