This study presents the development of an observing program to pursue the idea of looking for transiting exoplanets in eclipsing binary stars. The various kinds of orbits a planet might have in a binary system are explored. From this it is shown how to anticipate the possible orbits a planet might have in a given star system. The potential detectability of a planet in a binary system is also analyzed. Together these guidelines enable observers to rank targets by the likelihood that a detectable planet might exist in the system. The results of observations by a team at Ball State University of five binary star systems chosen with these guidelines are presented. / Department of Physics and Astronomy