Carbonates on large Solar System bodies like Earth and Mars (the latter represented by the meteorite ALH84001) form through the weathering of silicates in a watery (CO3)2- solution. The presence of carbonates in interplanetary dust particles and asteroids (again, represented by meteorites) is not completely understood, but has been attributed to aqueous alteration on a large parent body, which was subsequently shattered into smaller pieces. Despite efforts, the presence of carbonates outside the Solar System has hitherto not been established. Here we report the discovery of the carbonates calcite and dolomite in the dust shells of evolved stars, where the conditions are too primitive for the formation of large parent bodies with liquid water. These carbonates, therefore, are not formed by aqueous alteration, but perhaps through processes on the surfaces of dust or ice grains or gas phase condensation. The presence of carbonates which did not form by aqueous alteration suggests that some of the carbonates found in Solar System bodies no longer provide direct evidence that liquid water was present on large parent bodies early in the history of the Solar System.