A search for recoiling supermassive black hole candidates recently yielded the best candidate thus far, SDSS J092712.65+294344.0 reported by Komossa et al. Here we propose the alternative hypothesis that this object is a supermassive black hole binary. From the velocity shift imprinted in the emission-line spectrum we infer an orbital period of ~190 years for a binary mass ratio of 0.1, a secondary black hole mass of 100 million solar masses, and assuming inclination and orbital phase angles of 45 degrees. In this model the origin of the blueshifted narrow emission lines is naturally explained in the context of an accretion flow within the inner rim of the circumbinary disk. We attribute the blueshifted broad emission lines to gas associated with a disk around the accreting secondary black hole. We show that, within the uncertainties, this binary system can be long lived and thus, is not observed in a special moment in time. The orbital motion of the binary can potentially be observed with the VLBA if at least the secondary black hole is a radio emitter. In addition, for the parameters quoted above, the orbital motion will result in a ~100 km/s velocity shift of the emission lines on a time scale of about a year, providing a direct observational test for the binary hypothesis.