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Metamaterials are engineered media whose electromagnetic responses are different from those of their constituent components. They are often generated by incorporating in a periodic manner various types of artificially fabricated, extrinsic, low dimensional inhomogeneities in some background substrate. Double negative (DNG) metamaterials have both the permittivity and permeability negative. There have been a variety of antenna applications conceived and realized with various types of metamaterials. In this paper, we have investigated the possibility of matching an electrically small electric dipole to free space by surrounding it with a DNG shell. HFSS simulations confirm the resonant power gain predicted analytically and have given us insight into how a realistic electrically small efficient antenna (EESA) could be achieved.