The copolymerization of vinyl benzyl alcohol (VBA) and carbon monoxide (CO) to give a new polyester poly(VBA-CO) has been achieved via palladium-catalyzed hydroesterification. Reaction conditions involve moderate temperatures, moderate to low CO pressures, and low catalyst loadings to give a low molar mass (Mn 3-4 kg/mol) polymer as a 2:1 mixture of linear to branched repeat units. The polymer molar mass increase is consistent with a step-growth polymerization mechanism, and ester yields of >97% are achieved within 24 h. However, increases in Mn cease beyond 16 h. Control experiments indicate that the degree of polymerization is limited due to a combination of side reactions such as alcoholic end-group oxidation, hydroxycarbonylation, and alcohol acetylation, which lead to the degradation of monomeric and polymeric end groups. When a less promiscuous substrate is used such as 10-undecenol, higher molar masses (Mn 16 kg/mol) are achieved. This method has the potential to be a mild route to new polyester architectures with appropriate mitigation of side reactions.