The collapse of the Soufri¿re Hills Volcano lava dome on Montserrat in July 2003 is the largest such event worldwide in the historical record. Here we report on borehole dilatometer data recording a remarkable and unprecedented rapid (~600s) pressurisation of a magma chamber, triggered by this surface collapse. The chamber expansion is indicated by an expansive offset at the near dilatometer sites coupled with contraction at the far site. By analyzing the strain data and using added constraints from experimental petrology and long-term edifice deformation from GPS geodesy, we prefer a source centered at approximately 6 km depth below the crater for an oblate spheroid with overpressure increase of order 1 MPa and average radius ~1 km. Pressurisation is attributed to growth of 1--3% of gas bubbles in supersaturated magma, triggered by the dynamics of surface unloading. Recent simulations demonstrate that pressure recovery from bubble growth can exceed initial pressure drop by nearly an order of magnitude.