We have obtained an HI absorption spectrum of the relativistic binary PSR J1141-6545 and used it to constrain the distance to the system. The spectrum suggests that the pulsar is at, or beyond, the tangent point, estimated to be at 3.7 kpc. PSR J1141-6545 offers the promise of stringent tests of general relativity (GR) by comparing its observed orbital period derivative with that derived from other relativistic observables. At the distance of PSR J1141-6545 it should be possible to verify GR to an accuracy of just a few per cent, as contributions to the observed orbital period derivative from kinematic terms will be a small fraction of that induced by the emission of gravitational radiation. PSR J1141-6545 will thus make an exceptional gravitational laboratory.