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Abstract: Recently, a model for the preparation of ''protein-like'' heteropolymers with a unique and stable ground state has been proposed and examined computationally. Formally, this model is similar to another recently proposed and computationally examined model of the evolutionary design of protein-like heteropolymers. Using mean field replica theory, we find, in addition to the freezing transition of random chains, a transition to the target ''native'' state. The stability of this state is shown to be greater than that of the ground state of random chains. The results derived here should at least qualitatively be applicable to known biopolymers, which are conjectured to be in vivo ''designed'' by evolution. Furthermore, we present a crude prescription for a laboratory procedure in which chains can be synthesized in vitro