© 2017. The American Astronomical Society. All rights reserved. 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 Mg = -17.2. The maximum bolometric luminosity (from optical and UV) was Lp ≃ (1.0 ± 0.15) × 1043erg 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 ∝ e-(t-t0)/τ, where t0 = 57631.0 (MJD) and τ ≃ 15 days. The X-ray shows a marginal detection at LX = 2.41.9-1.1 × 1039 erg s-1 (Swift X-ray Telescope). No radio counterpart was detected down to 3σ, providing upper limits for monochromatic radio luminosities of νLν < 1.7 × 1036 erg s-1 and νLν < 2.3 × 1037 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.