Electrically conductive fibers are required for various applications in modern textile technology, e.g., the manufacturing of smart textiles and fiber composite systems with textile-based sensor and actuator systems. According to the state of the art, fine copper wires, carbon rovings, or metallized filament yarns, which offer very good electrical conductivity but low mechanical elongation capabilities, are primarily used for this purpose. However, for applications requiring highly flexible textile structures, as, for example, in the case of wearable smart textiles and fiber elastomer composites, the development of electrically conductive, elastic yarns is of great importance. Therefore, highly stretchable thermoplastic polyurethane (TPU) was compounded with electrically conductive carbon nanotubes (CNTs) and subsequently melt spun. The melt spinning technology had to be modified for the processing of highly viscous TPU–CNT compounds with fill levels of up to 6 wt.% CNT. The optimal configuration was achieved at a CNT content of 5 wt.%, providing an electrical resistance of 110 Ωcm and an elongation at break of 400%.