Boron nitride nanotubes (BNNTs) have attracted attention for their predicted extraordinary properties; yet, challenges in synthesis and processing have stifled progress on macroscopic materials. Recent advances have led to the production of highly pure BNNTs. Here we report that neat BNNTs dissolve in chlorosulfonic acid (CSA) and form birefringent liquid crystal domains at concentrations above 170 ppmw. These tactoidal domains merge into millimeter-sized regions upon light sonication in capillaries. Cryogenic electron microscopy directly shows nematic alignment of BNNTs in solution. BNNT liquid crystals can be processed into aligned films and extruded into neat BNNT fibers. This study of nematic liquid crystals of BNNTs demonstrates their ability to form macroscopic materials to be used in high-performance applications.