The discovery of superconductivity at temperatures above the boiling point of nitrogen has led to intense interest in the physics and chemistry of materials exhibiting this behaviour. Although some experiments can be performed on sintered polycrystalline samples, large single crystals are important for many measurements of physical properties, including investigations of the relationship between structural parameters and superconducting properties. Like its predecessors YB2Cu3O7 (refs 1-4) and La2-xSrxCuO4 (ref. 5), the recently discovered 84-K bismuth-strontium-calcium cuprate superconductor6-9 melts incon-gruently, and crystals have been grown from eutectic melts10. This technique yields crystals large enough for some experiments, but is generally difficult to control, placing limits on the size of crystals that can be grown. In addition, the crystals must be mechanically separated from the melt. Here we report the growth of single crystals of Bi2.2Sr 2Ca0.8Cu2O8+δ from alkali chloride fluxes. The crystals are superconductors, showing large Meissner effects and zero-resistance transitions above 80 K. Flux growth is a standard high-temperature solution growth technique, and should allow crystal size and quality to be controlled by parameters such as equilibration temperature, cooling rate and melt composition. The fluxes reported here are easily washed from the crystals.