Using carbon dioxide (CO2) as a feedstock for commodity synthesis is an attractive means of reducing greenhouse gas emissions and a possible stepping-stone towards renewable synthetic fuels(1,2). A major impediment to synthesizing compounds from CO2 is the difficulty of forming carbon-carbon (C-C) bonds efficiently: although CO2 reacts readily with carbon-centred nucleophiles, generating these intermediates requires high-energy reagents (such as highly reducing metals or strong organic bases), carbon-heteroatom bonds or relatively acidic carbon-hydrogen (C-H) bonds(3-5). These requirements negate the environmental benefit of using CO2 as a substrate and limit the chemistry to low-volume targets. Here we show that intermediate-temperature (200 to 350 degrees Celsius) molten salts containing caesium or potassium cations enable carbonate ions (CO32-) to deprotonate very weakly acidic C-H bonds (pK(a) > 40), generating carbon-centred nucleophiles that react with CO2 to form carboxylates. To illustrate a potential application, we use C-H carboxylation followed by protonation to convert 2-furoic acid into furan-2,5-dicarboxylic acid (FDCA)-a highly desirable bio-based feedstock(6) with numerous applications, including the synthesis of polyethylene furandicarboxylate (PEF), which is a potential large-scale substitute for petroleum-derived polyethylene terephthalate (PET)(7,8). Since 2-furoic acid can readily be made from lignocellulose9, CO32--promoted C-H carboxylation thus reveals a way to transform inedible biomass and CO2 into a valuable feedstock chemical. Our results provide a new strategy for using CO2 in the synthesis of multi-carbon compounds.