It is shown that structural disorder-in the form of anisotropic, picoscale atomic displacements-modulates the refractive index tensor and results in the giant optical anisotropy observed in BaTiS₃, a quasi-1D hexagonal chalcogenide. Single-crystal X-ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS₆ chains along the c-axis, and threefold degenerate Ti displacements in the a-b plane. ^47/49Ti solid-state NMR provides additional evidence for those Ti displacements in the form of a three-horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. Scanning transmission electron microscopy is used to directly observe the globally disordered Ti a-b plane displacements and find them to be ordered locally over a few unit cells. First-principles calculations show that the Ti a-b plane displacements selectively reduce the refractive index along the ab-plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS₃, this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity.