The recent transit observation of HD 209458 b - an extrasolar planet orbiting a sun-like star - confirmed that it is a gas giant and determined that its orbital inclination is 85 degrees. This inclination makes possible investigations of the planet atmosphere. In this paper we discuss the planet transmission spectra during a transit. The basic tenet of the method is that the planet atmosphere absorption features will be superimposed on the stellar flux as the stellar flux passes through the planet atmosphere above the limb. The ratio of the planet's transparent atmosphere area to the star area is small, approximately 10^{-3} to 10^{-4}; for this method to work very strong planet spectral features are necessary. We use our models of close-in extrasolar giant planets to estimate promising absorption signatures: the alkali metal lines, in particular the Na I and K I resonance doublets, and the He I $2^3S$ - $2^3P$ triplet line at 1083.0 nm. If successful, observations will constrain the line-of-sight temperature, pressure, and density. The most important point is that observations will constrain the cloud depth, which in turn will distinguish between different atmosphere models. We also discuss the potential of this method for EGPs at different orbital distances and orbiting non-solar-type stars.

revised to agree with accepted paper, ApJ, in press. 12 pages