We present a 77Se NMR study of the newly discovered iron selenide superconductor K(y)Fe(2-x)Se2, in which T(c) = 32 K. Below T(c), the Knight shift 77K drops sharply with temperature, providing strong evidence for singlet pairing. Above T(c), Korringa-type relaxation indicates Fermi-liquid behavior. Our experimental results set strict constraints on the nature of possible theories for the mechanism of high-T(c) superconductivity in this iron selenide system.