We experimentally demonstrate a chiral metamaterial exhibiting negative refractive index at terahertz frequencies. The presence of strong chirality in the terahertz metamaterial lifts the degeneracy for the two circularly polarized waves and allows for the achievement of negative refractive index without requiring simultaneously negative permittivity and negative permeability. The realization of terahertz chiral negative index metamaterials offers opportunities for investigation of their novel electromagnetic properties, such as negative refraction and negative reflection, as well as important terahertz device applications.