Supernovae have been confirmed to redshift z approximately 1.7 (refs 1, 2) for type Ia (thermonuclear detonation of a white dwarf) and to z approximately 0.7 (refs 1, 3-5) for type II (collapse of the core of the star). The subclass type IIn (ref. 6) supernovae are luminous core-collapse explosions of massive stars and, unlike other types, are very bright in the ultraviolet, which should enable them to be found optically at redshifts z approximately 2 and higher. In addition, the interaction of the ejecta with circumstellar material creates strong, long-lived emission lines that allow spectroscopic confirmation of many events of this type at z approximately 2 for 3-5 years after explosion (ref. 14). Here we report three spectroscopically confirmed type IIn supernovae, at redshifts z = 0.808, 2.013 and 2.357, detected in archival data using a method designed to exploit these properties at z approximately 2. Type IIn supernovae directly probe the formation of massive stars at high redshift. The number found to date is consistent with the expectations of a locally measured stellar initial mass function, but not with an evolving initial mass function proposed to explain independent observations at low and high redshift.