We find the supergravity solution sourced by a supertube: a (1/4)-supersymmetric D0-charged IIA superstring that has been blown up to a cylindrical D2-brane by angular momentum. The supergravity solution captures all essential features of the supertube, including the D2-dipole moment and an upper bound on the angular momentum: violation of this bound implies the existence of closed timelike curves, with a consequent ghost-induced instability of supertube probes.