We have designed and built a single‐crystal fiber growth apparatus. The apparatus employs novel optical, mechanical, and electronic control systems that enable the growth of high optical quality single‐crystal fibers. We have grown oriented single‐crystal fibers of four refractory oxide materials, Al2O3, Cr:Al2O3, Nd:YAG, and LiNbO3. These materials exhibit similar growth characteristics and yield fibers of comparable quality. Fibers as small as 20 &mgr;m in diameter and as long as 20 cm have been grown. Measured optical losses at 1.06 &mgr;m for a 10‐cm‐long, 170‐&mgr;m‐diam Cr:Al2O3fiber were 0.074 dB/cm.