A model which describes the competition between chain melting and orientational ordering in a monomolecular layer of long-chain amphiphilic molecules is studied. This model is analogous to the Berker-Cardy-Nelson-Scalapino model for phase transitions in films of 3He-4He mixtures. Their Midgal-Kadanoff renormalization-group approach is applied to the present problem. It reveals two phase transitions. A first-order one, associated with the melting of hydrophobic chains and a Kosterlitz-Thouless-type transition linked to the existence of topological orientational order of the chains in the high-molecular-area region. Isotherms and coexistence curves in the region of the liquid-expanded liquid-condensed transition are calculated. The disagreement with experimental results suggests that the model does not adequately describe the phase transition. This is in contradiction with a previous suggestion based on mean-field considerations.