GRBs are thought to arise in relativistic blast-wave shocks at distances of 10 to 1000 AU from the point where the explosive energy is initially released. To account for the observed duration and variability of the gamma-ray emission in most GRBs, a central engine powering the shocks must remain active for several seconds to many minutes but must strongly fluctuate in its output on much shorter timescales. We show how a neutron star differentially rotating at millisecond periods (DROMP) could be such an engine. A magnetized DROMP would repeatedly wind up toroidal magnetic fields to about 10**17 G and only release the corresponding magnetic energy, when each buoyant magnetic field torus floats up to, and breaks through, the stellar surface. The resulting rapid sub-bursts, separated by relatively quiescent phases, repeat until the kinetic energy of differential rotation is exhausted by these events. Calculated values of the energy released and of the various timescales are in agreement with observations of GRBs. The baryon loading in each sub-burst may also be consistent with theoretical requirements for a blast wave capable of giving the X-ray, optical and radio afterglows recently observed from cosmological distances. DROMPs could be created in several kinds of astrophysical events; some of these would be expected to occur at about the observed GRB rate. The requisite differential rotation could be imparted to neutron stars as they are born or at the end of their existence: some DROMPs may be created close to star forming regions while others may arise far from galaxies.

6 pages, 1 figure