Over 40% of Sun-like stars are bound in binary or multistar systems. Stellar remnants in edge-on binary systems can gravitationally magnify their companions, as predicted 40 years ago. By using data from the Kepler spacecraft, we report the detection of such a "self-lensing" system, in which a 5-hour pulse of 0.1% amplitude occurs every orbital period. The white dwarf stellar remnant and its Sun-like companion orbit one another every 88.18 days, a long period for a white dwarf-eclipsing binary. By modeling the pulse as gravitational magnification (microlensing) along with Kepler's laws and stellar models, we constrain the mass of the white dwarf to be similar to 63% of the mass of our Sun. Further study of this system, and any others discovered like it, will help to constrain the physics of white dwarfs and binary star evolution.