We report new constraints on the local escape speed of our Galaxy. Our analysis is based on a sample of high velocity stars from the RAVE survey and two previously published datasets (the Geneva-Copenhagen survey and the Beers et al. catalogue of metal-poor stars). We use cosmological simulations of disk galaxy formation to motivate our assumptions on the shape of the velocity distribution, allowing for a significantly more precise measurement of the escape velocity compared to previous studies. We find that the escape velocity lies within the range 492 km s−1 < vesc <594 kms (90% confidence), with a median likelihood of 536 kms. The fact that v2esc is significantly greater than 2v2circ implies that there must be a significant amount of mass exterior to the Solar circle, i.e. this convincingly demonstrates the presence of a dark halo in the Galaxy. For a simple isothermal halo, one can calculate that the minimum radial extent is ~54 kpc. We use our constraints on vesc to determine the mass of the Milky Way halo for three halo profiles. For example, an adiabatically contracted NFW halo model results in a virial mass of 1.31+0.97−0.49 × 1012M⊙ and virial radius of 297+60−44 kpc (90% confidence). For this model the circular velocity at the virial radius is 141+27−19kms. Although our halo masses are model dependent, we find that they are in good agreement with each other.