Almost every galaxy, including our Milky Way, has a supermassive black hole at its heart, with masses of millions to billions of times the mass of the Sun. The hierarchical nature of galaxy formation suggests that a supermassive black hole binary should be common, and may exist even in our own galactic center. We propose a new approach to constraining the possible orbital configuration of such a binary companion to the galactic center black hole Sagittarius A* (Sgr A*) through the measurement of stellar orbits. Focusing on the star S0-2, we show that requiring its orbital stability in the presence of a companion to Sgr A* yields stringent constraints on such a companion's possible configurations. Using existing data on S0-2 we derive upper limits on the binary black hole separation as a function of the companion mass. If such a companion exists, it will emit gravitational wave radiation, potentially detectable with the Laser Interferometer Space Antenna (LISA).