We present two epochs of radial velocities of the first imaged T dwarf Gliese 229 B obtained with Keck/NIRSPEC. The two radial velocities are discrepant with one another and with the radial velocity of the host star, at ≈11σ significance. This points to the existence of a previously postulated, but as-yet undetected, massive companion to Gl 229 B; we denote the two components as Gl 229 Ba and Gl 229 Bb. We compute the joint likelihood of the radial velocities to constrain the period and mass of the secondary companion. Our radial velocities are consistent with an orbital period between a few days and ≈60 days, and a secondary mass of at least ≈15 M Jup and up to nearly half the total system mass of Gl 229 B. With a significant fraction of the system mass in a faint companion, the strong tension between Gl 229 B’s dynamical mass and the predictions of evolutionary models is resolved.