Alkali metal carboxylates, including sodium acetate, sodium benzoate, and sodium sorbate, which are all readily available and widely used as food additives, were found to promote the ring-opening polymerization (ROP) of trimethylene carbonate (TMC) to produce poly(trimethylene carbonate) (PTMC). The sodium acetate-catalyzed ROP of TMC proceeded in the presence of an alcohol initiator under solvent-free conditions at 70 °C, even at very low catalyst loadings of 0.01–0.0001 mol%. The controlled nature of this ROP system enabled the synthesis of PTMCs with predicted molecular weights ranging from 2400 to 11 700 g mol−1 and narrow dispersities (~1.23). Importantly, ROP is initiated by an alcohol initiator, allowing PTMC production with desired functional groups, such as azido, alkyne, and methacrylate groups, at the α-chain end. Furthermore, the poly(L-lactic acid)-b-PTMC-b-poly(L-lactic acid) triblock copolymer, a biodegradable thermoplastic elastomer, was successfully synthesized in one pot via the sodium acetate-catalyzed ring-opening block copolymerization of TMC and L-lactide with a 1,3-propanediol initiator.