Many of the physical properties of the copper oxide high-temperature superconductors appear to defy the conventional 'one-electron' theory of metals. The development of alternative theories incorporating strong electron correlations is currently at the forefront of research in condensed-matter physics. In this context, inelastic neutron scattering can provide valuable insight into collective magnetic excitations in the copper oxide super-conductors and so guide these theoretical efforts. Such measurements require large single crystals, and have hitherto been restricted to just two families of high-temperature superconductors-La2-x Srx CuO4 and YBa2 Cu3 O6+x. Although the magnetic spectra of these two materials bear certain similarities, there are also important differences. In particular, a sharp resonant spin excitation dominates the spectrum in the superconducting state of YBa2 Cu3 O6+x[3-10], but is not observed in La2-x Srx CuO4. Here we report inelastic neutron scattering measurements of a different copper oxide system-Bi2 Sr2 CaCu2 O8 + delta - in which we observe a magnetic resonance peak in the superconducting state. This result implies that this excitation phenomenon is a general feature of the copper oxide superconductors, so extending the empirical basis for its theoretical description.