Using optical second-harmonic generation, we have studied the orientational order of cyanobiphenyl liquid-crystal monolayers at the interface between a mica crystal and a liquid-crystal film put in the presence of ethylene glycol vapor. These small, volatile molecules adsorb at the mica surface and significantly affect the orientational order of the surface liquid-crystal molecules. As the chemical potential of the volatile molecules was increased, this orientational order first varied continuously, and at a certain stage, exhibited a discontinuous change corresponding to a first-order orientational transition. This surface transition drives the first-order anchoring transition (i.e., the reorientation of the bulk liquid crystal) previously observed in these systems.