In this paper we describe a lattice density functional theory for the rotator-herringbone phase transition in a liquid supported monolayer system of long chain acids or alcohols. It is assumed that both phases have long-range translational order and that the rotator phase is characterized by a uniform distribution of backbone orientation. We find that orientational interactions among the backbone planes an sufficient to drive a second order transition, and we characterize the phase of the system by a parameter associated with the width of the peaks in a distribution which describes the orientations of the backbones. We also briefly discuss generalizations of the theory to include lattice vibrations and distortions.