By using a true phasor approach and slowly varying envelope approximations along with Maxwell’s equations and the constitutive relations in their respective domains (time and frequency, respectively), we derive expressions for the allowable propagation vector(s), electromagnetic fields, Poynting vectors, phase, energy, and group velocities in a medium where independent material parameters such as permittivity, permeability, and chirality are frequency dependent, including not only the carrier (e.g., optical) frequency but excursions around the carrier. One definition of negative index, viz., contradirection of the propagation and Poynting vector, demands a large value for the chirality parameter, which may not be physically attainable. We show that by incorporating dispersions in these (independent) material parameters, it may be possible to achieve negative index as defined through contradirected phase and group velocities for a range of carrier frequencies that are lower than the resonant frequency for the aforementioned material parameters as described through the Lorenz (for permittivity and permeability) and Condon (for chirality) models, and without violating the upper bound on the chirality. This has the added advantage that losses will be minimal, and further justifies our approach of using real functions for the material parameters.