The operation of a reactor on an open but self-sustainable cycle without actinide separation is known as breed-and-burn. It has mostly been envisioned for use in solid-fueled fast-spectrum reactors such as sodium-cooled fast reactors. In this paper the applicability of breed-and-burn to molten salt reactors is investigated first on a cell level using a modified neutron excess method. Several candidate fuel salts are selected and their performance in a conceptual three-dimensional reactor is investigated. Chloride-fueled single-fluid breed-and-burn molten salt reactors using enriched chlorine are shown to be feasible from a neutronics and fuel cycle point of view at the cost of large fuel inventories.