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We demonstrate the biocompatibility of carbon nanotube fibers (CNFs) fabricated from single-wall carbon nanotubes. Produced by a particle-coagulation spinning process, CNFs are "hair-like" conductive microwires, which uniquely combine properties of porous nanostructured scaffolds, high-area electrodes, and permeable microfluidic conduits. We report that CNFs are nontoxic and support the attachment, spreading, and growth of mammalian cells and the extension of processes from neurons in vitro. Our findings suggest that CNF may be employed for an electrical interfacing of nerve cells and external devices.