We demonstrate the first rewritable memory in thermally drawn fibers. A high tellurium-content chalcogenide glass, contacted by metallic electrodes internal to the fiber structure, is drawn from a macroscopic preform. An externally applied voltage is utilized to switch between a high resistance (OFF) and a low resistance (ON) state; this in turn allows the fibers to function as a memory device reminiscent of the ovonic switch. The difference between the ON and OFF states is found to be four orders of magnitude. The glass–crystal phase transition is localized to micrometer-wide filaments, whose position can be optically controlled along the fiber axis. An architecture that enabled the encoding of multiple bits per fiber is described.