We show that optical second-harmonic generation (SHG) can be observed from individual single-walled carbon nanotubes (SWCNTs) and, furthermore, allows imaging of individual tubes. Detailed analysis of our results suggests that the structural non-centrosymmetry, as required for SHG, arises from the non-zero chiral angle of the SWCNT. SHG thus has potential as a fast,non-destructive and simple method for imaging of individual nanomolecules and for probing their chiral properties.