For ten years, planets around stars similar to the Sun have been discovered, confirmed, and their properties studied. Planets have been found in a variety of environments previously thought impossible. The results have revolutionized the way in which scientists understand planet and star formation and evolution, and provide context for the roles of the Earth and our own solar system. Over half of star systems contain more than one stellar component. Despite this, binary stars have often been avoided by programs searching for planets. Discovery of giant planets in compact binary systems would indirectly probe the timescales of planet formation, an important quantity in determining by which processes planets form. A new observing method has been developed to perform very high precision differntial astrometry on bright binary stars with separations in the range of 0.1 - 1.0 arcseconds. Typical measurement precisions over an hour of integration are on the order of 10 micro-arcseconds (as), enabling one to look for perturbations to the Keplerian orbit that would indicate the presence of additional components to the system. This method is used as the basis for a new program to find extrasolar planets. The Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) is a search for giant planets orbiting either star in 50 binary systems. The goal of this search is to detect or rule out planets in the systems observed and thus place limits on any enhancements of planet formation in binaries. It is also used to measure fundamental properties of the stars comprising the binary, such as masses and distances, useful for constraining stellar models at the 10-3 level.