Volcanic eruptions are episodic despite being supplied by melt at a nearly constant rate. We used histories of magma efflux and surface deformation to geodetically image magma transfer within the deep crustal plumbing of the Soufrière Hills volcano on Montserrat, West Indies. For three cycles of effusion followed by discrete pauses, supply of the system from the deep crust and mantle was continuous. During periods of reinitiated high surface efflux, magma rose quickly and synchronously from a deflating mid-crustal reservoir (at about 12 kilometers) augmented from depth. During repose, the lower reservoir refilled from the deep supply, with only minor discharge transiting the upper chamber to surface. These observations are consistent with a model involving the continuous supply of magma from the deep crust and mantle into a voluminous and compliant mid-crustal reservoir, episodically valved below a shallow reservoir (at about 6 kilometers).