We present a model for a coupled magma chamber–dike system to investigate the conditions required to initiate volcanic eruptions and to determine what controls the size of eruptions. The model combines the mechanics of dike propagation with internal chamber dynamics including crystallization, volatile exsolution, and the elastic response of the magma and surrounding crust to pressure changes within the chamber. We find three regimes for dike growth and eruptions: (1) below a critical magma chamber size, eruptions are suppressed because chamber pressure drops to lithostatic before a dike reaches the surface; (2) at an intermediate chamber size, the erupted volume is less than the dike volume (“dike-limited” eruption regime); and (3) above a certain chamber size, dikes can easily reach the surface and the erupted volume follows a classic scaling law, which depends on the attributes of the magma chamber (“chamber-limited” eruption regime). The critical chamber volume for an eruption ranges from ∼0.01 km3 to 10 km3 depending on the water content in the magma, depth of the chamber, and initial overpressure. This implies that the first eruptions at a volcano likely are preceded by a protracted history of magma chamber growth at depth, and that the crust above the magma chamber may have trapped several intrusions or “failed eruptions.” Model results can be combined with field observations of erupted volume, pressure, and crystal and volatile content to provide tighter constraints on parameters such as the eruptible chamber size.