Researchers have argued for many years that one of the conditions for omnidirectional reflection in a one-dimensional photonic crystal is a strong refractive index contrast between the two constituent dielectric materials. Using numerical simulations and the theory of Anderson localization of light, in this work we demonstrate that an omnidirectional band gap can indeed be created utilizing low refractive index contrast materials when they are arranged in a disordered manner. Moreover, the size of the omnidirectional band gap becomes a controllable parameter, which now depends on the number of layers and not only on the refractive index contrast of the system, as it is widely accepted. This achievement constitutes a major breakthrough in the field since it allows for the development of cheaper and more efficient technologies. Of particular interest is the case of high index contrast one-dimensional photonic crystal fibers, where the propagation losses are mainly due to increased optical scattering from sidewall roughness at the interfaces of high index contrast materials. By using low index contrast materials these losses can be reduced dramatically, while maintaining the confinement capability of the waveguide. This is just one of many applications that could be proven useful for this discovery.