We have measured the indices of refraction and dielectric constants along different directions in thin films of the crystalline organic semiconductor compound 3, 4, 9, 10 perylenetetracarboxylic dianhydride (PTCDA). The films were deposited via organic molecular beam deposition, resulting in single‐crystalline, ‘‘quasi‐epitaxial’’ films. Due to inherent asymmetries in the molecular crystal structure, film ordering results in giant anisotropies in their dielectric properties. For example, the index of refraction measured at a wavelength of λ=1.064 μm in the direction perpendicular to the substrate plane is n⊥ = 1.36 ± 0.01, whereas parallel to the plane, n∥=2.017±0.005, resulting in an index difference of Δn=0.66. Furthermore, the low‐frequency dielectric constant of the films is ϵ⊥ = 1.9 ± 0.1 and ϵ∥ = 4.5 ± 0.2. To our knowledge, these are the largest anisotropies ever measured for thin films. We discuss a guided wave polarization‐selective device which takes advantage of the large dielectric anisotropies characteristic of the thin organic films.