We report the discovery of ASASSN-15lh (SN 2015L), which we interpret as the most luminous supernova yet found. At redshift z = 0.2326, ASASSN-15lh reached an absolute magnitude of M-u,M-AB = -23.5 +/- 0.1 and bolometric luminosity L-bol = (2.2 +/- 0.2) x 10(45) ergs s(-1), which is more than twice as luminous as any previously known supernova. It has several major features characteristic of the hydrogen-poor super-luminous supernovae (SLSNe-I), whose energy sources and progenitors are currently poorly understood. In contrast to most previously known SLSNe-I that reside in star-forming dwarf galaxies, ASASSN-15lh appears to be hosted by a luminous galaxy (M-K approximate to -25.5) with little star formation. In the 4 months since first detection, ASASSN-15lh radiated (1.1 +/- 0.2) x 10(52) ergs, challenging the magnetar model for its engine.