An inelastic neutron scattering study of overdoped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 83 K) has revealed a resonant spin excitation in the superconducting state. The mode energy is E(res) = 38.0 meV, significantly lower than in optimally doped Bi(2)Sr(2)CaCu(2)O(8+delta) ( T(c) = 91 K, E(res) = 42.4 meV). This observation, which indicates a constant ratio E(res)/k(B)T(c) approximately 5.4, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high temperature superconductors.