AMPHIPHILIC molecules, which contain a polar ’head’ group and a hydrophobic ’tail’, will generally form monolayers at the air-water interface in which the molecules protrude from the interface with the tails in the air. These ’Langmuir monolayers’ exhibit a variety of phases as a function of surface pressure and temperature, including an ordered, two-dimensional crystalline phase1-3. It might be considered that the amphiphilic nature of the molecules allows this oriented, tail up arrangement and the consequent formation of a well ordered phase. Here, by contrast, we report that the nonpolar molecule perfluoro-n-eicosane (F(CF2)20F) will form stable, ordered Langmuir monolayers on water, even though they have no amphiphilic character. Grazing-incidence X-ray diffraction studies of these monolayers show that the molecules are vertically aligned and are packed in a hexagonal array over a range of temperature. We suggest that van der Waals forces alone are sufficient to stabilize the monolayer in this case.