AN UNUSUAL astronomical source of hard X-ray bursts, GRO J1744 - 28, was discovered recently(1,2). The properties of this source differ markedly from those of other known high-energy burst sources-X-ray bursters, soft gamma-ray repeaters and gamma-ray bursters- suggesting that it may represent a new type of source. The bursts probably arise from unstable accretion of matter onto a compact object(2), such as a neutron star, but the nature of the object and the origin of the burst instability have not been revealed by observations of the bursts themselves. Here we report the detection of coherent X-ray pulsations, with a period of 467 milliseconds, from GRO J1744 - 28; these are the first persistent pulsations seem in a bursting X-ray source. These pulses and their timing indicate that the object is a magnetized neutron star, accreting gas from a low-mass companion star. The pulsation rate has been increasing during the period of our observations, indicating that an accretion disk has been formed and that the transfer of matter from the disk is spinning up the neutron star. The source of the instability that leads to the bursts remains unknown.