The ground state of a rigid chain molecular model for Langmuir monolayers is investigated. Model molecules are made lip of two rigid chains of "atoms" interacting by Lennard-Jones potentials. It is found out that a minimum of the interaction energy occurs when the molecules are in a herringbone configuration with (nearest neighbor) tilted chains. Upon increasing the applied surface pressure the model displays a reorientation of chains towards next nearest neighbors, resembling that observed in some real surfactant monolayers. At higher pressure the model also displays a, 2-nd order transition to an untilted state.