We obtain, by making use of the anomaly term in the divergence of the flavor-singlet axial-vector-current, new spectral-function sum rules for the pseudoscalar density in a chiral-SU(3) × SU(3) × U3(1) framework. The positivity conditions on the spectral representations of the pseudoscalar densitites lead to a new bound on the quark-condensate term 0|q»q|0<-(279 MeV)3 (q=u, d, and s) corresponding to bare-current-quark values of mu=md5 MeV and m150 MeV. © 1983 The American Physical Society.