We report the observation of strong third-harmonic generation from a macroscopic array of aligned ultralong single-wall carbon nanotubes (SWCNTs) with intense midinfrared radiation. Through power-dependent experiments, we determined the absolute value of the third-order nonlinear optical susceptibility (3) of our SWCNT film to be 5.5310-12 esu, three orders of magnitude larger than that of the fused silica reference we used. Taking account of the filling factor of 8.75% for our SWCNT film, we estimate a (3) of 6.3210-11 esu for a fully dense film. Furthermore, through polarization-dependent experiments, we extracted all the nonzero elements of the (3) tensor, determining the magnitude of the weaker tensor elements to be 1/6 of that of the dominant zzzz(3) component. 2013 American Physical Society.