In a Langmuir monolayer made of pure fluorescent NBD stearic acid, an ordered anisotropic phase was observed. The molecular structure of this solid phase was determined by electron scattering after transfer of the layer onto a solid substrate by the usual Langmuir-Blodgett technique. The electron diffraction pattern shows sharp peaks, indicating two-dimensional long-range positional order. The diffraction pattern is analyzed by comparison with Fourier transforms of models of molecular arrangements. The simulations reveal that the aliphatic chains are positioned along parallel strips, in agreement with optical studies.