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We present ground-based and Swift observations of iPTF16fnl, a likely tidal disruption event (TDE) discovered by the intermediate Palomar Transient Factory (iPTF) survey at 66.6 Mpc. The light curve of the object peaked at an absolute mag ${M}_{g}=-17.2$. The maximum bolometric luminosity (from optical and UV) was ${L}_{p}\simeq (1.0\pm 0.15)\times {10}^{43}$ erg s⁻¹, an order of magnitude fainter than any other optical TDE discovered so far. The luminosity in the first 60 days is consistent with an exponential decay, with $L\propto {e}^{-(t-{t}_{0})/\tau }$, where t₀ = 57631.0 (MJD) and $\tau \simeq 15$ days. The X-ray shows a marginal detection at ${L}_{X}={2.4}_{-1.1}^{1.9}\times {10}^{39}$ erg s⁻¹ (Swift X-ray Telescope). No radio counterpart was detected down to 3σ, providing upper limits for monochromatic radio luminosities of ${\nu L}_{\nu }\lt 2.3\times {10}^{36}$ erg s⁻¹ and ${\nu L}_{\nu }\lt 1.7\times {10}^{37}$ erg s⁻¹ (Very Large Array, 6.1 and 22 GHz). The blackbody temperature, obtained from combined Swift UV and optical photometry, shows a constant value of 19,000 K. The transient spectrum at peak is characterized by broad He ii and Hα emission lines, with FWHMs of about 14,000 km s⁻¹ and 10,000 km s⁻¹, respectively. He i lines are also detected at λλ 5875 and 6678. The spectrum of the host is dominated by strong Balmer absorption lines, which are consistent with a post-starburst (E+A) galaxy with an age of ∼650 Myr and solar metallicity. The characteristics of iPTF16fnl make it an outlier on both luminosity and decay timescales, as compared to other optically selected TDEs. The discovery of such a faint optical event suggests a higher rate of tidal disruptions, as low-luminosity events may have gone unnoticed in previous searches.