We investigate ice shelf rift propagation using a combination of GPS and seismic measurements near the tip of an active rift in the Amery Ice Shelf. These measurements reveal that propagation occurs in episodic bursts, which were identified based on swarms of seismicity accompanied by rapid rift widening. The bursts last approximately 4 hours and are separated by 10--24 days. In between bursts, the rift widens at a rate comparable to that of ice shelf spreading. Comparison of automatic weather station data and tidal amplitudes show that the propagation bursts are not directly triggered by winds or tides, suggesting that rift propagation is driven by the background glaciological stress in the ice shelf. We show that the ice debris that partly fills the rift may play a role in controlling the rate of propagation.