Electrospinning of a polyelectrolyte and vapor deposition polymerization were combined to fabricate nanotubes of oxidatively stabilized poly(acrylonitrile) (PAN Delta) with an outer diameter of 100 nm, a wall thickness of 14 nm, and centimeter-scale length. Poly(styrene sulfonate) sodium (PSSNa) nanofibers serves as sacrificial cores while vapor deposition polymerization was used to form smooth PAN sheaths of even thickness. After the PAN sheaths had been oxidatively stabilized, the PSSNa cores were etched away with water to form nanotubes of PAN Delta. High-temperature carbonization of these nanotubes at 900 degrees C under Ar flow yielded carbon nanotubes with an outer diameter of 80 nm and wall thickness of 10 nm. Raman spectroscopy confirms that the carbon nanotubes were composed of highly disordered graphene sheets, consistent with the carbonization of PAN under similar conditions. These carbon nanotubes have many promising applications as catalyst supports, gas absorbents, and as encapsulants for controlled release of active compounds.