Negative refractive index is introduced in metamaterials whereby the Poynting vector of the electromagnetic (EM) wave is in opposition to the group velocity, or alternatively, when the group and phase velocities in the medium are in opposition. In recent years, considerable research has been carried out relative to the EM propagation and refraction characteristics in metamaterials with emphasis on the origins of negative refractive index. The latter phenomenon has been extensively investigated in the literature, including recent work involving chiral metamaterials with material dispersion up to the first and second orders. An EM propagation in a chiral, dispersive material up to the first order is examined for possible emergence of negative refractive index under non-conductive losses. Three loss scenarios are considered, viz., dielectric losses (complex permittivity), magnetic losses (complex permeability), and a combination of both types of losses. A spectral approach combined with a slowly time-varying phasor analysis is applied, leading to the analytic derivation of EM phase and group velocities and corresponding indices. The velocities and indices are examined by selecting arbitrary dispersion parameters based on published practical values. The results indicate the emergence of negative index within specific radio frequency modulation bands. The resulting polarization states of the fields are examined under loss conditions. Finally, a method is suggested whereby the effects of dielectric and magnetic losses may be combined via appropriate Taylor coefficients such that the effective attenuation constant may be driven to zero via induced gain mechanisms arising from the dielectric and magnetic loss models.