The magnetic excitation spectrum of a YBa2Cu3O7 crystal containing 0.5% of nonmagnetic (Zn) impurities has been determined by inelastic neutron scattering. Whereas in the pure system a sharp resonance peak at E . 40 meV is observed exclusively below the superconducting transition temperature Tc, the magnetic response in the Zn-substituted system is broadened significantly and vanishes at a temperature much higher than Tc. The energy-integrated spectral weight observed near q › sp, pd increases with Zn substitution, and only about half of the spectral weight is removed at Tc. [S0031-9007(99)08563-4]