Galaxy mergers play a key role in the evolution of galaxies and the growth of their central supermassive black holes ( SMBHs ) . A search for ( active ) SMBH binaries ( SMBHBs ) at the centers of the merger remnants is currently ongoing . Perhaps the greatest challenge is to identify the inactive SMBHBs , which might be the most abundant , but are also the most difficult to identify . Liu et al . predicted characteristic drops in the light curves of tidal disruption events ( TDEs ) , caused by the presence of a secondary SMBH . Here , we apply that model to the light curve of the optically inactive galaxy SDSS J120136.02+300305.5 , which was identified as a candidate TDE with XMM-Newton . We show that the deep dips in its evolving X-ray light curve can be well explained by the presence of a SMBHB at its core . A SMBHB model with a mass of the primary of M _ { BH } = 10 ^ { 7 } M _ { \sun } , a mass ratio q \simeq 0.08 , and a semimajor axis a _ { b } \simeq 0.6 { mpc } is in good agreement with the observations . Given that primary mass , introducing an orbital eccentricity is needed , with e _ { b } \simeq 0.3 . Alternatively , a lower mass primary of M _ { BH } = 10 ^ { 6 } M _ { \sun } in a circular orbit fits the light curve well . Tight binaries like this one , which have already overcome the “ final parsec problem , ” are prime sources of gravitational wave radiation once the two SMBHs coalesce . Future transient surveys , which will detect TDEs in large numbers , will place tight constraints on the SMBHB fraction in otherwise non-active galaxies .