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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.