We report the detection of CO(1-0) emission from NGC 1277, a lenticular galaxy in the Perseus Cluster. NGC 1277 has previously been proposed to host an overmassive black hole (BH) compared to the galaxy bulge luminosity (mass), based on stellar-kinematic measurements. The CO(1-0) emission, observed with the IRAM Plateau de Bure Interferometer (PdBI) using both, a more compact (2.9-arcsec resolution) and a more extended (1-arcsec resolution) configuration, is likely to originate from the dust lane encompassing the galaxy nucleus at a distance of 0.9 arcsec (∼320 pc). The double-horned CO(1-0) profile found at 2.9-arcsec resolution traces 1.5 × 108 M⊙ of molecular gas, likely orbiting in the dust lane at ∼550 km s−1, which suggests a total enclosed mass of ∼2 × 1010 M⊙. At 1-arcsec resolution, the CO(1-0) emission appears spatially resolved along the dust lane in east–west direction, though at a low signal-to-noise ratio. In agreement with the previous stellar-kinematic measurements, the CO(1-0) kinematics is found to be consistent with an ∼1.7 × 1010 M⊙ BH for a stellar mass-to-light ratio of M/LV = 6.3, while a less massive BH of ∼5 × 109 M⊙ is possible when assuming a larger M/LV = 10. While the molecular gas reservoir may be associated with a low level of star formation activity, the extended 2.6-mm continuum emission is likely to originate from a weak AGN, possibly characterized by an inverted radio-to-millimetre spectral energy distribution. Literature radio and X-ray data indicate that the BH in NGC 1277 is also overmassive with respect to the Fundamental Plane of BH activity.