  Stars with initial masses 10 M_{solar} < M_{initial} < 100 M_{solar} fuse
progressively heavier elements in their centres, up to inert iron. The core
then gravitationally collapses to a neutron star or a black hole, leading to an
explosion -- an iron-core-collapse supernova (SN). In contrast, extremely
massive stars (M_{initial} > 140 M_{solar}), if such exist, have oxygen cores
which exceed M_{core} = 50 M_{solar}. There, high temperatures are reached at
relatively low densities. Conversion of energetic, pressure-supporting photons
into electron-positron pairs occurs prior to oxygen ignition, and leads to a
violent contraction that triggers a catastrophic nuclear explosion. Tremendous
energies (>~ 10^{52} erg) are released, completely unbinding the star in a
pair-instability SN (PISN), with no compact remnant. Transitional objects with
100 M_{solar} < M_{initial} < 140 M_{solar}, which end up as iron-core-collapse
supernovae following violent mass ejections, perhaps due to short instances of
the pair instability, may have been identified. However, genuine PISNe, perhaps
common in the early Universe, have not been observed to date. Here, we present
our discovery of SN 2007bi, a luminous, slowly evolving supernova located
within a dwarf galaxy (~1% the size of the Milky Way). We measure the exploding
core mass to be likely ~100 M_{solar}, in which case theory unambiguously
predicts a PISN outcome. We show that >3 M_{solar} of radioactive 56Ni were
synthesized, and that our observations are well fit by PISN models. A PISN
explosion in the local Universe indicates that nearby dwarf galaxies probably
host extremely massive stars, above the apparent Galactic limit, perhaps
resulting from star formation processes similar to those that created the first
stars in the Universe.
