Single-wall carbon nanotubes (SWCNT) of diameter 1.3 nm have been produced and cut into finite lengths centered at 160 nm. A solution of them in DMF has been prepared for third-order optical non-linearity measurements using the femtosecond optical Kerr effect at a wavelength of 820 nm. The ultrafast second-order hyperpolarizability, gamma, of this SWCNT is estimated to be as large as 2.1 X 10(-28) esu.