We present a technique to study depth profiles of molecular orientation in soft matter thin films with nanometer resolution. The method is based on dichroism in resonant soft X-ray reflectivity using linear s- and p-polarization. It combines the chemical sensitivity of Near-Edge X-ray Absorption Fine Structure spectroscopy to specific molecular bonds and their orientation relative to the polarization of the incident beam with the precise depth profiling capability of X-ray reflectivity. We demonstrate these capabilities on side chain liquid crystalline polymer thin films with soft X-ray reflectivity data at the carbon K edge. Optical constants of the anisotropic refractive index ellipsoid were obtained from a quantitative analysis using the Berreman formalism. For films up to 50 nm thickness we find that the degree of orientation of the long axis exhibits no depth variation and is
independent of the film thickness.