The cytoplasmic heritable determinant [ PSI ⁺ ] of the yeast Saccharomyces cerevisiae reflects the prion-like properties of the chromosome-encoded protein Sup35p. This protein is known to be an essential eukaryote polypeptide release factor, namely eRF3. In a [ PSI ⁺ ] background, the prion conformer of Sup35p forms large oligomers, which results in the intracellular depletion of functional release factor and hence inefficient translation termination. We have investigated the process by which the [ PSI ⁺ ] determinant can be efficiently eliminated from strains, by growth in the presence of the protein denaturant guanidine hydrochloride (GuHCl). Strains are “cured” of [ PSI ⁺ ] by millimolar concentrations of GuHCl, well below that normally required for protein denaturation. Here we provide evidence indicating that the elimination of the [ PSI ⁺ ] determinant is not derived from the direct dissolution of self-replicating [ PSI ⁺ ] seeds by GuHCl. Although GuHCl does elicit a moderate stress response, the elimination of [ PSI ⁺ ] is not enhanced by stress, and furthermore, exhibits an absolute requirement for continued cell division. We propose that GuHCl inhibits a critical event in the propagation of the prion conformer and demonstrate that the kinetics of curing by GuHCl fit a random segregation model whereby the heritable [ PSI ⁺ ] element is diluted from a culture, after the total inhibition of prion replication by GuHCl.