In this paper the problem of designing a polymer repeat unit with fine-tuned or optimized thermophysical and mechanical properties is addressed. The values of these properties are estimated using group contribution methods based on the number and type of the molecular groups participating in the polymer repeat unit. By exploiting the prevailing mathematical features of the structure-property relations the following two research objectives are addressed : (i) How to efficiently locate a ranked list of the best polymer repeat unit architectures with mathematical certainty; and (ii) how to quantify the effect of imprecision in property estimation in the optimal design or polymers. A blend of mixed-integer linear optimization, chance-constrained programming, and multilinear regression is utilized to answer these questions. The proposed methodology is highlighted with a illustrative example. Preliminary results (see also Maranas (1996a,b)) demonstrate that the proposed framework identifies the the mathematically best molecular design and quantifies the profound effect that property prediction uncertainty may have in optimal molecular design.