We demonstrate that the differential ac-Stark shift of a Zeeman-sensitive ground hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the |2S1/2,F=2,mF=-2> to the |2S1/2,F=1,mF=-1> state of 7Li to observe 0.59±0.02  Hz linewidth with interrogation time of 2 s and 0.82±0.06  s coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed.

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