  The hierarchical nature of galaxy formation suggests that a supermassive
black hole binary could exist in our galactic center. We propose a new approach
to constraining the possible orbital configuration of such a binary companion
to the galactic center black hole 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 the
possible configurations of such a companion. Furthermore, we show that precise
measurements of {\it time variations} in the orbital parameters of S0-2 could
yield stronger constraints. Using existing data on S0-2 we derive upper limits
on the binary black hole separation as a function of the companion mass. For
the case of a circular orbit, we can rule out a 10^5 M_sun companion with a
semimajor axis greater than 170 astronomical units or 0.8 mpc. This is already
more stringent than bounds obtained from studies of the proper motion of Sgr
A*. Including other stars orbiting the galactic center should yield stronger
constraints that could help uncover the presence of a companion to Sgr A*. We
show that a companion can also affect the accretion process, resulting in a
variability which may be consistent with the measured infrared flaring
timescales and amplitudes. Finally, if such a companion exists, it will emit
gravitational wave radiation, potentially detectable with LISA.
