We report on electrooptic measurements on Langmuir-Blodgett (LB) monolayers of a 1/1 mixture of n-octyl-cyanobiphenyl (8CB) and stearic acid. The required sensitivity is achieved by depositing the LB-film on a thin gold layer and measuring the field-induced shift of the surface plasmon resonance. The existence of a finite electrooptic coefficient is proof of polar anisotropy in the monolayer. The electrooptic coefficient depends on details of the deposition process and does not change with temperature or frequency of the applied electric field.