A complementary bilayer cross-wire chiral metamaterial is proposed and studied experimentally and numerically. It exhibits giant optical activity and a small circular dichroism. The retrieval results reveal that a negative refractive index is realized for right circularly polarized waves due to the strong chirality. Our numerical results show that the mechanism of the chiral behavior at the resonance of lower frequency can be interpreted as the coupling effects between two sets of mutually twisted virtual magnetic dipoles, while the resonance of higher frequency shows complicated nonlocal features.