The best-studied dike intrusion events on a divergent plate boundary occurred along the Krafla segment of the northern rift zone in Iceland from 1975--1984. Seismic and geodetic measurements there showed that a central magma chamber fed dikes that propagated laterally many times the thickness of the lithosphere. The patterns of dike length, dike width, caldera subsidence, and lava extrusion strongly suggest that dike propagation is affected by tectonic stresses that change with each dike intrusion event and that magma pressures are linked to the dike opening. These observations have inspired us to develop a quantitative model for the lateral propagation of basaltic dikes away from a magma chamber. We assume dikes propagate as long as there is sufficient driving pressure, defined as the difference between magma pressure and tectonic stress at the dike tip. The opening dike and the magma chamber are treated as a closed system for a given dike intrusion event. During an event, magma pressure is reduced linearly with the magma volume withdrawn from the chamber. Relative tectonic tension in the lithosphere is reduced linearly as the dike width increases. A dike begins propagation when the driving pressure equals the "breakout" pressure needed to force the magma out of the chamber. It stops when the driving pressure reaches a minimum value. Generally, the dike width is proportional to this "stopping" pressure, and a reasonable value gives a width of 1 m. Besides the breakout and stopping pressures, the propagation distance depends on the initial distribution of tectonic stress and the thickness of the lithosphere cut by a dike. The intrusion of a dike changes the tectonic stress distribution so that subsequent dikes may propagate different distances and directions than the first dike. After a period of magma chamber refilling, a new dike can initiate if the breakout pressure is reached. For an idealized spreading segment the tectonic stress field evolves to produce a sequence of dikes propagating in one direction followed by a sequence of dikes propagating in the opposite direction. The first dike in each sequence should be the longest followed by successively shorter dikes. When tectonic stresses close to a magma chamber have been largely relieved, then extrusion of magma may start. The model pattern of dike propagation and extrusion is consistent with data from the Krafla episode. Magma chamber size should have a major effect on magmatic systems in other tectonic settings with larger magma chambers producing longer characteristic dikes.