The theoretical maximum tensile strain — that is, elongation — of a single-walled carbon nanotube is almost 20%, but in practice only 6% is achieved. Here we show that, at high temperatures, individual single-walled carbon nanotubes can undergo superplastic deformation, becoming nearly 280% longer and 15 times narrower before breaking. This superplastic deformation is the result of the nucleation and motion of kinks in the structure, and could prove useful in helping to strengthen and toughen ceramics and other nanocomposites at high temperatures.