Stars with initial masses such that 10<=M$_initial$<=100, where 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$_initial$>=140 (if such exist) develop oxygen cores with masses, M$_core$, that exceed 50, 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 100<M$_initial$<140 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 SN2007bi, a luminous, slowly evolving object located within a dwarf galaxy. We estimate the exploding core mass to be M$_core$åisebox-0.5ex 100, in which case theory unambiguously predicts a pair-instability supernova. We show that >3 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.