  We present the results of the first systematic search for spectroscopic
binaries within the central 2 x 3 arcsec$^2$ around the supermassive black hole
at the center of the Milky Way galaxy. This survey is based primarily on over a
decade of adaptive optics-fed integral-field spectroscopy (R$\sim$4000),
obtained as part of the Galactic Center Orbits Initiative at Keck Observatory,
and has a limiting $K$'-band magnitude of 15.8, which is at least 4 magnitudes
deeper than previous spectroscopic searches for binaries at larger radii within
the central nuclear star cluster. From this primary dataset, over 600 new
radial velocities are extracted and reported, increasing by a factor of 3 the
number of such measurements. We find no significant periodic signals in our
sample of 28 stars, of which 16 are massive, young (main-sequence B) stars and
12 are low-mass, old (M and K giant) stars. Using Monte Carlo simulations, we
derive upper limits on the intrinsic binary star fraction for the young star
population at 47% (at 95% confidence) located $\sim$20 mpc from the black hole.
The young star binary fraction is significantly lower than that observed in the
field (70%). This result is consistent with a scenario in which the central
supermassive black hole drives nearby stellar binaries to merge or be disrupted
and may have important implications for the production of gravitational waves
and hypervelocity stars.
