WE report the discovery of a millisecond pulsar in the globular cluster 47 Tucanae (NGC104). It has a spin period of 4.479 ms and is a member of a binary system with an orbital period of 32 min and an eccentricity of 0.32. The mass function, 2.9 x 10-8Msolar, is the smallest value for any known binary system. We find that the observations are consistent with a neutron star of mass 1.4 Msolar and a white-dwarf companion of mass 0.8 Msolar. The millisecond spin period combined with the very short orbital period offers, for the first time, the possibility of observing spin-orbit coupling effects predicted by general relativity theory.