The stability of heavy nuclides, which tend to decay by α-emission and spontaneous fission, is determined by the structural properties of nuclear matter. Nuclear binding energies and lifetimes increase markedly in the vicinity of closed shells of neutrons or protons (nucleons), corresponding to `magic' numbers of nucleons; these give rise to the most stable (spherical) nuclear shapes in the ground state. For example, with a proton number of Z = 82 and a neutron number of N = 126, the nucleus 208Pb is `doubly-magic' and also exceptionally stable. The next closed neutron shell is expected at N = 184, leading to the prediction of an `island of stability' of superheavy nuclei, for a broad range of isotopes with Z = 104 to 120 (refs 1, 2). The heaviest known nuclei have lifetimes of less than a millisecond, but nuclei near the top of the island of stability are predicted to exist for many years. (In contrast, nuclear matter consisting of about 300 nucleons with no shell structure would undergo fission within about 10-20 seconds.) Calculations indicate that nuclei with N > 168 should already benefit from the stabilizing influence of the closed shell at N = 184. Here we report the synthesis of an isotope containing 114 protons and 173 neutrons, through fusion of intense beams of 48Ca ions with 242Pu targets. The isotope decays by α-emission with a half-life of about five seconds, providing experimental confirmation of the island of stability.