Quantum-mechanical systems have information processing capabilities(1,2) that are not possible with classical devices, One example is quantum teleportation(3), in which the quantum state of a system is transported from one location to another without moving through the intervening space. But although partial implementations(4,5) of quantum teleportation over macroscopic distances have been achieved using optical systems, the final stage of the teleportation procedure-which allows the complete recovery of the original state-was omitted. Here we report an experimental implementation of full quantum teleportation over interatomic distances using liquid-state nuclear magnetic resonance. We achieve teleportation of the quantum state of a carbon nucleus to a hydrogen nucleus in molecules of trichloroethylene, by exploiting natural phase decoherence of the carbon nuclei. Such a teleportation scheme may be used as a subroutine in larger quantum computations, or for quantum communication.