The drawing of glass fibers from preform rods is restricted, by gravity-induced sagging of the molten glass, to a narrow range of viscosity/pulling speed combinations. A scaling analysis of the forces acting on the elongating melt indicates that the absence of gravity would extend this range and permit the drawing of low viscosity melts to form glass-clad single crystal fibers and crystallite-free fibers of glasses such as ZBLAN. Therefore, fiber drawing in microgravity could yield cost-effective products such as ultra-low-loss infrared fibers. Fiber drawing experiments are ideally suited for Shuttle/Spacelab missions, because of their short duration, moderate power demands, and insensitivity to g-jitter, and can even be advantageously performed in lunar gravity. To facilitate such experiments, a prototype spaceflight apparatus has been developed, under NASA sponsorship, that occupies less than 0.16 m3 of volume and weighs less than 27 kg.