  Many physical properties of the copper oxide high temperature superconductors
appear to defy the conventional (one-electron) theory of metals, and the
development of new theories incorporating strong electron correlations is
currently at the forefront of condensed matter physics. Inelastic neutron
scattering provides incisive information about collective magnetic excitations
that is required to guide this effort. Such measurements have thus far proven
possible for only two of the many families of high temperature superconductors,
La_{2-x} Sr_x CuO_4 and YBa_2 Cu_3 O_{6+x},because suitably large single
crystals of other copper oxide compounds could not be grown. While the magnetic
spectra of both materials bear certain similarities, there are also pronounced
differences that have hampered a unified description of the spin dynamics in
the copper oxides. In particular, a sharp resonant spin excitation dominates
the spectrum in the superconducting state of YBa_2 Cu_3 O_{6+x}, but is not
found in La_{2-x} Sr_x CuO_4. Here we report the discovery of a magnetic
resonance peak in the superconducting state of a different copper oxide system,
Bi_2 Sr_2 Ca Cu_2 O_{8+\delta}, made possible by the synthesis of a sizable
single crystal and modern neutron optics. This provides evidence of the
generality of this unusual phenomenon among the copper oxides and greatly
extends the empirical basis for its theoretical description.
