Neutron diffraction and heat capacity measurements are combined to study the structures and phase transitions occurring in a monolayer of fluoromethane physically adsorbed on graphite. Neutron diffraction reveals two solid phases with a phase transition between 100 and 105 K and melting of the layer between 120 and 130 K. The unit cells of both phases are determined to be commensurate with the underlying substrate (3 × √3) with lattice parametersa= 0·738 nm,b= 0·426 nm and β = 90·0°, and both contain two molecules in the unit cell. The heat capacity is determined for the monolayer between 0·5 and 150 K. There is a sharp anomaly corresponding to melting at 124 K and a small anomaly around 100 K corresponding to an order-order transition, both consistent with the diffraction results. An additional anomaly is observed around 140 K, where the film is in the liquid phase. At very low temperatures there is evidence of tunnelling splitting of the librational ground state with a value of 10 μeV, smaller than that in bulk CH3F. The low-temperature heat capacity also gives a value of 30 K for the ‘gap’ in the phonon density of states arising from the commensurate structure of the layer. The normal heat capacity is also analysed to obtain average characteristic temperatures for the different molecular motions.