We perform second-harmonic generation (SHG) microscopy with circularly polarized (CP) light to measure chirality of individual twisted-cross gold nanodimers. The chiral signatures, based on different SHG response for the two CP components of incident light, are clearly visible even with off-resonance excitation. The SHG responses of individual nanodimers are found to vary by about a factor of five. The technique thus has very high sensitivity to the nanoscale deformations of the structure. The chiral signatures of the dimers, however, are found to be more uniform, and the technique is thus able to recognize the handedness of the twisted nanodimers with high reliability.