We report the design and fabrication of a multilayered macroscopic fiber preform and the subsequent drawing and optical characterization of extended lengths of omnidirectional dielectric mirror fibers with submicrometer layer thickness. A pair of glassy materials with substantially different indices of refraction, but with similar thermomechanical properties, was used to construct 21 layers of alternating refractive index surrounding a tough polymer core. Large directional photonic band gaps and high reflection efficiencies comparable to those of the best metallic reflectors were obtained. Potential applications of these fibers include woven fabrics for radiation barriers, spectral authentication of cloth, and filters for telecommunications.