Stars with initial masses such that 10M[symbol: see text] <or= M(initial) <or= 100M[symbol: see text], where M[symbol: see text] is the solar mass, fuse progressively heavier elements in their centres, until the core is inert iron. The core then gravitationally collapses to a neutron star or a black hole, leading to an explosion-an iron-core-collapse supernova. By contrast, extremely massive stars with M(initial) >or= 140M[symbol: see text] (if such exist) develop oxygen cores with masses, M(core), that exceed 50M[symbol: see text], where high temperatures are reached at relatively low densities. Conversion of energetic, pressure-supporting photons into electron-positron pairs occurs before oxygen ignition and leads to a violent contraction which triggers a nuclear explosion that unbinds the star in a pair-instability supernova. Transitional objects with 100M[symbol: see text] < M(initial) < 140M[symbol: see text] may end up as iron-core-collapse supernovae following violent mass ejections, perhaps as a result of brief episodes of pair instability, and may already have been identified. Here we report observations of supernova SN 2007bi, a luminous, slowly evolving object located within a dwarf galaxy. We estimate the exploding core mass to be M(core) approximately 100M[symbol: see text], in which case theory unambiguously predicts a pair-instability supernova. We show that >3M[symbol: see text] of radioactive (56)Ni was synthesized during the explosion and that our observations are well fitted by models of pair-instability supernovae. This indicates that nearby dwarf galaxies probably host extremely massive stars, above the apparent Galactic stellar mass limit, which perhaps result from processes similar to those that created the first stars in the Universe.