Cu63 nuclear quadrupole resonance (NQR) has been observed in the ternary compound CeCu2Si2 which, when stoichiometric, is a heavy-fermion superconductor. In a superconducting specimen (Tc0.6 K) the observed temperature dependence of the spin-lattice relaxation rate 1T1(T) is consistent with a conventional quasiparticle excitation spectrum below Tc, with a pair-breaking parameter approximately half the value for suppression of superconductivity. Features in 1T1(T) between Tc and 1.2 K appear to signal a phase transition, possibly structural in nature. NQR data from a nonsuperconducting sample are consistent with extensive disorder in the Cu site occupation. © 1984 The American Physical Society.