PHBV is produced by bacteria as intracellular carbon storage. It is advantageous concerning biocompatibility and biodegradability, but its low crystallization rate hinders the melt-processing of fibers. This problem can be overcome by combining PHBV with PLA in a core/sheath configuration and introducing a new spin pack concept. The resulting PHBV/PLA bicomponent fibers show an ultimate tensile stress of up to 0.34 GPa and an E-modulus of up to 7.1 GPa. XRD reveals that PLA alone is responsible for tensile strength. In vitro biocompatibility studies with human fibroblasts reveal good cytocompatibility, making these fibers promising candidates for medical therapeutic approaches.