Black hole binary systems with companion stars are typically found via their x-ray emission, generated by interaction and accretion. Noninteracting binaries are expected to be plentiful in the Galaxy but must be observed using other methods. We combine radial velocity and photometric variability data to show that the bright, rapidly rotating giant star 2MASS J05215658+4359220 is in a binary system with a massive unseen companion. The system has an orbital period of ~83 days and near-zero eccentricity. The photometric variability period of the giant is consistent with the orbital period, indicating star spots and tidal synchronization. Constraints on the giant’s mass and radius imply that the unseen companion is 3.3-0.7+2.8 solar masses, indicating that it is a noninteracting low-mass black hole or an unexpectedly massive neutron star.