The physical basis for the transparency of the cornea to visible light is investigated theoretically in terms of the molecular structure as depicted by electron microscopy. Electron micrographs show that the major portion of the cornea contains long cylindrical fibrils arranged in a quasi-random fashion, with local order extending over distances comparable to the wavelength of light. Heretofore, the generally accepted explanation of transparency has been in terms of a supposed crystalline arrangement of the fibrils, because this was the only distribution that could ensure transparency on a simple theoretical basis. Thus, the non-crystalline structure shown by the electron microscope has been widely regarded as an artifact due to the fixation procedure. In the present work, the light scattering from the fibrils is formulated in terms of their radial distribution function, which is determined by numerical analysis of electron micrographs. Comparison of theoretical results and experimental values for transmittance through rabbit cornea shows that the quasi-regular quasi-random structure revealed by the electron microscope is not in conflict with transparency.