ASASSN-14ae is a candidate tidal disruption event (TDE) found at the center of SDSS J110840.11+340552.2 ($dsimeq200$~Mpc) by the All-Sky Automated Survey for Supernovae (ASAS-SN). We present ground-based and Swift follow-up photometric and spectroscopic observations of the source, finding that the transient had a peak luminosity of $Lsimeq8times10^{43}$~erg~s$^{-1}$ and a total integrated energy of $Esimeq1.7times10^{50}$ ergs radiated over the $sim5$ months of observations presented. The blackbody temperature of the transient remains roughly constant at $Tsim20,000$~K while the luminosity declines by nearly 1.5 orders of magnitude during this time, a drop that is most consistent with an exponential, $Lpropto e^{-t/t_0}$ with $t_0simeq39$~days. The source has broad Balmer lines in emission at all epochs as well as a broad He II feature emerging in later epochs. We compare the color and spectral evolution to both supernovae and normal AGN to show that { ame} does not resemble either type of object and conclude that a TDE is the most likely explanation for our observations. At $z=0.0436$, ASASSN-14ae is the lowest-redshift TDE candidate discovered at optical/UV wavelengths to date, and we estimate that ASAS-SN may discover $0.1 - 3$ of these events every year in the future.
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