Dual color four-wave-mixing (FWM) microscopy is used to spatially resolve the third-order optical response from individual carbon nanotubes. Good signal-to-noise is obtained from single-walled carbon nanotubes (SWNT) sitting on substrates, when the excitation beams are resonant with electronic transitions of the nanotube, by detecting the FWM response at the anti-Stokes frequency. Whereas the coherent anti-Stokes (CAS) signal is sensitive to both electronic and vibrational resonances of the material, it is shown that the signal from individual SWNTs is dominated by the electronic response. The CAS signal is strongly polarization dependent, with the highest signals found parallel with the enhanced electronic polarizibility along the long axis of the SWNT.