  ASASSN-14ae is a candidate tidal disruption event (TDE) found at the center
of SDSS J110840.11+340552.2 ($d\simeq200$~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 $L\simeq8\times10^{43}$~erg~s$^{-1}$ and a
total integrated energy of $E\simeq1.7\times10^{50}$ ergs radiated over the
$\sim5$ months of observations presented. The blackbody temperature of the
transient remains roughly constant at $T\sim20,000$~K while the luminosity
declines by nearly 1.5 orders of magnitude during this time, a drop that is
most consistent with an exponential, $L\propto e^{-t/t_0}$ with
$t_0\simeq39$~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 {\name}
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.
