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, $χ^{(3)}$, of our SWCNT film to be 5.53 $\times$ 10$^{-12}$ 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 $χ^{(3)}$ of 6.32 $\times$ 10$^{-11}$ esu for a fully dense film. Furthermore, through polarization-dependent experiments, we extracted all the nonzero elements of the $χ^{(3)}$ tensor, determining the magnitude of the weaker tensor elements to be $∼$1/6 of that of the dominant $χ^{(3)}_{zzzz}$ component. ; Comment: 5 pages, 3 figures