We present the first results of a spectroscopic survey of M, L, and T dwarfs being conducted with the Infrared Spectrograph onboard the Spitzer Space Telescope. We observed GJ 1001 A (M3.5 V), DENIS 0255-4700 (L8.0 V), and is an element of Ind Ba/Bb (T1/T6 V). As expected from the predictions of model atmospheres, the spectra show absorption features of H2O, CH4 at 7.8 mu m, and NH3 at 10.5 mu m. This is the first detection of the 7.8 mu m CH4 band and the first secure detection of NH3 in the spectra of brown dwarfs. Finally, we compute the bolometric luminosities of three of the dwarfs in our sample by combining 0.6-4.1 mu m spectra with the Spitzer spectra and find good agreement with previous results that use L'-and M'-band photometry to account for the flux emitted between 2.5 and 5 mu m.