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We have developed a process for fabricating silica nanowires with a diameter of only one thousandth the diameter of a hair. Although significantly narrower than the wavelength of light, these nanowires can act as "rails" for light. About half the optical energy is outside the wire, is sensitive to its environment, a property useful for chemical and biological sensors. The wires allow single-mode operation and have very low optical losses within the visible to near-infrared spectral range. Mechanical tests show that the wires have tensile strength in excess of 5 GPa -- stronger than spider silk. The wires are also resilient and flexible, easily bending into microscopic loops. When combined with other devices such as nanoscale lasers, the wires may provide opportunities for a variety of applications ranging from optical communications to microsurgery.