Here we report timing measurements of the relativistic binary pulsar PSR J1141-6545 that constrain the component masses and demonstrate that the orbital period derivative \dot Pb = (-4+/-1)x10^-13 is consistent with gravitational wave emission as described by the general theory of relativity. The mass of the neutron star and its companion are 1.30+/-0.02 Mo and 0.986+/-0.020 Mo respectively, suggesting a white dwarf companion, and extending the range of systems for which general relativity provides a correct description. On evolutionary grounds, the progenitor mass of PSR J1141-6545 should be near the minimum for neutron star production. Its mass is two standard deviations below the mean of the other neutron stars, suggesting a relationship between progenitor and remnant masses. Comment: 10 pages, 2 figures, revised version to Ap J Letters