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 (d≃216 Mpc) by the All-Sky Automated Survey for SuperNovae (ASAS-SN). The source peaked at a bolometric luminosity of L≃1.9×1044 ergs s−1 and radiated a total energy of E≃5.0×1050 ergs over the ∼3.5 months of observations. The early optical/UV emission of the source can be fit by a blackbody with temperature increasing from T∼2×104 K to T∼6×104 K while the luminosity declines from L≃1.9×1044 ergs s−1 to L≃2.8×1043 ergs s−1, requiring the photosphere to be shrinking rapidly. The optical/UV luminosity decline is broadly consistent with an exponential decline, L∝e−t/t0, with t0≃35 days. 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 ∼3 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