The star S0-2, which orbits the supermassive black hole (SMBH) in our Galaxy with a period of 16 years, provides the strongest constraint on both the mass of the SMBH and the distance to the Galactic center. S0-2 will soon provide the first measurement of relativistic effects near a SMBH. We report the first limits on the binarity of S0-2 from radial velocity (RV) monitoring, which has implications for both understanding its origin and robustness as a probe of the central gravitational field. With 87 RV measurements, which include 12 new observations that we present, we have the requisite data set to look for RV variations from S0-2's orbital model. Using a Lomb-Scargle analysis and orbit- fitting for potential binaries, we detect no RV variation beyond S0-2's orbital motion and do not find any significant periodic signal. The lack of a binary companion does not currently distinguish different formation scenarios for S0-2. The upper limit on the mass of a companion star (M_comp_) still allowed by our results has a median upper limit of M_comp_ sin i <=1.6M_{sun}_ for periods between 1 and 150 days, the longest period to avoid tidal break-up of the binary. We also investigate the impact of the remaining allowed binary system on the measurement of the relativistic redshift at S0-2's closest approach in 2018. While binary star systems are important to consider for this experiment, we find that plausible binaries for S0-2 will not alter a 5{sigma} detection of the relativistic redshift.