An optical interferometer capable of tracking phase and measuring fringe visibility has demonstrated the ability to measure the precise positions of stars over large angles. This instrument has tracked phase over periods of many hours while switching sequentially among several stars. The 3.1 m separation of the siderostats has been m~asured to an accuracy of 50 ,u, indicating positional accuracies of 3 arcsec. The formal error of the least-squares solution for the baselines is of the order of a micron. The major limitations to accuracy were thermal instabilities and unmonitored siderostat positions. With improvements, this technique should be capable of astrometric accuracies exceeding one-hundredth of an arcsecond. Two small mirrors, Si and S2, intercept light from a star which is combined at beam spiitter BS and detected at photodetector P. The variable delay line DL makes interference fringes possible by adjusting for the difference between the two path lengths from the beam splitter to the stellar wave front via each arm of the interferometer. This adjustment, commonly called the delay, must change with time in order to compensate for the rotation of the Earth when tracking celestial sources, as well as to track out atmospheric turbulence. The fringe pattern, i.e., the intensity of the light at the photodetector as a function of delay, is proportional to the Fourier transform of the optical bandpass of the system. The sensitivity of the interferometer is proportional to the