We present a new electromagnetic phenomenon-the asymmetric second-harmonic generation from planar chiral structures. The effect consists in distinguishing the handedness of a chiral material by rotating the sample in an experiment involving solely linearly polarized light. This phenomenon originates in the surface plasmon resonance of chiral gold nanostructures, where homodyne interference of anisotropic and chiral electric and/or magnetic multipoles appears to play an important role.