The reactivity, speciation and solvation structure of CO2 in carbonate melts are relevant both for the fate of carbon in deep geological formations and for its electroreduction to CO, to be used as fuel, by means of solvation in a molten carbonate electrolyte. In particular, the high solubility of CO2 in carbonate melts has been tentatively attributed to the formation of a new carbon species, the pyrocarbonate anion, C_2O_5^{2−}. In this work we study, by first principles molecular dynamics simulations, the behaviour of CO2 in molten calcium carbonate. We find that pyrocarbonate forms spontaneously and the identity of the CO2 molecule is quickly lost through O^{2−} exchange. The transport of CO2 in this molten carbonate thus occurs in a fashion similar to the Grotthuss mechanism in water, and is three times faster than molecular diffusion. This shows that Grotthuss-like transport is more general than thought so far.