The newly discovered planet GJ 1214b is the first known transiting super-Earth requiring a significant atmosphere to explain its observed mass and radius. Models for the structure of this planet predict that it likely possesses a H-He envelope of at least 0.05% of the total mass of the planet. However, models without a significant H-He atmosphere are not entirely ruled out by the available data. Here we present transmission and emission spectra for the planet GJ 1214b. We explore a range of possible atmospheres for the planet, ranging from solar composition gas, to pure CO2 or water (steam). We find that, if GJ 1214b possesses a hydrogen-rich atmosphere as expected, then the primary transit depth for such an atmosphere would vary at a level of up to 0.3% as a function of wavelength, relative to the background light of its M-dwarf host star. Observations at this level of precision are potentially obtainable with current space-based instrumentation. Successful detection of the transmission signature of this planet at the ~0.1% level would therefore provide confirmation of the hydrogen-rich nature of the planetary atmosphere. It follows that transmission spectroscopy at this level of precision could provide a first glimpse into answering the question of whether planets in the super-Earth mass regime (1 - 10 M_Earth) more closely resemble large terrestrial planets or small gas giant planets.