We present ground-based and Swift photometric and spectroscopic observations of the candidate tidal disruption event (TDE) ASASSN-14li, found at the centre of PGC 043234 (d ... 90 Mpc) by the All-Sky Automated Survey for SuperNovae (ASAS-SN). The source had a peak bolometric luminosity of ... and a total integrated energy of ... erg radiated over the ~6 months of observations presented. The UV/optical emission of the source is well fitted by a blackbody with roughly constant temperature of T ... 35,000 K, while the luminosity declines by roughly a factor of 16 over this time. The optical/UV luminosity decline is broadly consistent with an exponential decline, ..., with t0 ... 60 d. ASASSN-14li also exhibits soft X-ray emission comparable in luminosity to the optical and UV emission but declining at a slower rate, and the X-ray emission now dominates. Spectra of the source show broad Balmer and helium lines in emission as well as strong blue continuum emission at all epochs. We use the discoveries of ASASSN-14li and ASASSN-14ae to estimate the TDE rate implied by ASAS-SN, finding an average rate of ... per galaxy with a 90 per cent confidence interval of ... per galaxy. ASAS-SN found roughly 1 TDE for every 70 Type Ia supernovae in 2014, a rate that is much higher than that of other surveys. (ProQuest: ... denotes formulae/symbols omitted.)