We have used fluorescence microscopy to observe the effect of shear on rigid two-dimensional structures residing in a Langmuir monolayer. Monolayers of 12-NBD stearic acid undergo a two-dimensional liquid-to-solid transition on the water surface. The domains of the solid phase that form in the coexistence region are elongated (needle-shaped) crystallites. We observe the effect of shear within the monolayer in two geometries: two-dimensional Poiseuille flow and simple shear flow created by moving bands. The technique allows us to determine the average orientational order parameter as well as the details of the rotational kinematics, which are, as expected, well-described by a Jeffery orbit. We propose that this technique of direct observation in Langmuir monolayers will be a useful method for the study of systems of rigid particles under flow.