  The theoretical mechanism for realizing the negative refractive index with
{\it electromagnetically induced transparency} (EIT) is studied. It is shown
that in a three-level dense atomic gas, there is a frequency band in which the
EIT medium will exhibit simultaneously negative electric permittivity and
magnetic permeability in the optical frequency range, and the atomic gas thus
becomes a left-handed material. The expressions for the electric permittivity
and the magnetic permeability for the probe frequency is presented. One of the
remarkable features of the present novel scheme is such that the obtained EIT
left-handed material is {\it isotropic} and may therefore have some potentially
important applications in the development of new techniques in quantum optics.
