We present ground-based and Swift photometric and spectroscopic observations of the tidal disruption event (TDE) ASASSN-15oi, discovered at the center of 2MASX J20390918-3045201 ($dsimeq216$ Mpc) by the All-Sky Automated Survey for SuperNovae (ASAS-SN). The source peaked at a bolometric luminosity of $Lsimeq1.3times10^{44}$ ergs s$^{-1}$ and radiated a total energy of $Esimeq6.6times10^{50}$ ergs over the first $sim3.5$ months of observations. The early optical/UV emission of the source can be fit by a blackbody with temperature increasing from $Tsim2times10^4$ K to $Tsim4times10^4$ K while the luminosity declines from $Lsimeq1.3times10^{44}$ ergs s$^{-1}$ to $Lsimeq2.3times10^{43}$ ergs s$^{-1}$, requiring the photosphere to be shrinking rapidly. The optical/UV luminosity decline during this period is most consistent with an exponential decline, $Lpropto e^{-(t-t_0)/tau}$, with $tau simeq46.5$ days for $t_0simeq57241.6$ (MJD), while a power-law decline of $Lpropto (t-t_0)^{-alpha}$ with $t_0simeq57212.3$ and $alpha=1.62$ provides a moderately worse fit. ASASSN-15oi also exhibits roughly constant soft X-ray emission that is significantly weaker than the optical/UV emission. Spectra of the source show broad helium emission lines and strong blue continuum emission in early epochs, although these features fade rapidly and are not present $sim3$ months after discovery. The early spectroscopic features and color evolution of ASASSN-15oi are consistent with a TDE, but the rapid spectral evolution is unique among optically-selected TDEs.
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