Tidal disruption events (TDEs), in which stars are gravitationally disrupted as they pass close to the supermassive black holes in the centres of galaxies, are potentially important probes of strong gravity and accretion physics. Most TDEs have been discovered in large-area monitoring surveys of many 1000s of galaxies, and the rate deduced for such events is relatively low: one event every 10$^4$ - 10$^5$ years per galaxy. However, given the selection effects inherent in such surveys, considerable uncertainties remain about the conditions that favour TDEs. Here we report the detection of unusually strong and broad helium emission lines following a luminous optical flare (Mv < -20.1 mag) in the nucleus of the nearby ultra-luminous infrared galaxy F01004-2237. The particular combination of variability and post-flare emission line spectrum observed in F01004-2237 is unlike any known supernova or active galactic nucleus. Therefore, the most plausible explanation for this phenomenon is a TDE -- the first detected in a galaxy with an ongoing massive starburst. The fact that this event has been detected in repeat spectroscopic observations of a sample of 15 ultra-luminous infrared galaxies over a period of just 10 years suggests that the rate of TDEs is much higher in such objects than in the general galaxy population.
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