Magma chamber volume is critical for volcano monitoring and forecasting. Standard geodetic methods cannot constrain the total volume, only the change in volume. Here, we show that stress perturbations associated with trapdoor faulting allow bounds to be placed on the total chamber volume at Sierra Negra volcano, in the Galapagos. The deformation response of the magma chamber to faulting depends on both the absolute chamber volume and the compressibility of the magma. Bubble-free magma provides the lower limit on compressibility, thus an upper bound on the chamber volume of 13.6 to 20.6 km³, depending on fault dip. We estimate an upper limit on compressibility using a conduit model relating volatile content to lava fountain height, which is compared with observations from the 2005 eruption, constrained by volatile content of olivine melt inclusions. This yields a lower bound on chamber volume of 0.5 times the upper bound.