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This paper studies the electromagnetic response of a coherently driven dense atomic ensemble to a weak probe. It finds that negative refraction with little absorption may be achieved in the presence of local-field enhanced interaction and dynamically induced chirality. The complex refractive index governing the probe refraction and absorption depends critically on the atomic density, the steady population distribution, the coherence dephasings, and the frequency detunings, and is also sensitive to the phase of the driving field because the photonic transition paths form a close loop. Thus, it can periodically tune the refractive index at a fixed frequency from negative to positive values and vice versa just by modulating the driving phase. Moreover, the optimal negative refraction is found to be near the probe magnetic resonance, which then requires the electric fields of the probe and the drive being on two-photon resonance due to the dipole synchronisation. [ABSTRACT FROM AUTHOR]