We present 2.12-2.23 Delta *mm high contrast integral field spectroscopy of the extrasolar planet HR 8799 b. Our observations were obtained with OSIRIS on the Keck II telescope and sample the 2.2 Delta *mm CH4 feature, which is useful for spectral classification and as a temperature diagnostic for ultracool objects. The spectrum of HR 8799 b is relatively featureless, with little or no methane absorption, and does not exhibit the strong CH4 seen in T dwarfs of similar absolute magnitudes. The spectrum is consistent with field objects from early-L to T4 (3 Delta *s confidence level), with a best-fitting type of T2. A similar analysis of the published 1-4 Delta *mm photometry shows the infrared spectral energy distribution (SED) matches L5-L8 field dwarfs, especially the reddest known objects which are believed to be young and/or very dusty. Overall, we find that HR 8799 b has a spectral type consistent with L5-T2, although its SED is atypical compared to most field objects. We fit the 2.2 Delta *mm spectrum and the infrared SED using the Hubeny & Burrows, Burrows et al., and Ames-Dusty model atmosphere grids, which incorporate non-equilibrium chemistry, non-solar metallicities, and clear and cloudy variants. No models agree with all of the data, but those with intermediate clouds produce significantly better fits. The largest discrepancy occurs in the J band, which is highly suppressed in HR 8799 b. Models with high eddy diffusion coefficients and high metallicities are somewhat preferred over those with equilibrium chemistry and solar metallicity. The best-fitting effective temperatures range from 1300 to 1700 K with radii between ~0.3 and 0.5 R Jup. These values are inconsistent with evolutionary model-derived values of 800-900 K and 1.1-1.3 R Jup based on the luminosity of HR 8799 b and the age of HR 8799, a discrepancy that probably results from imperfect atmospheric models or the limited range of physical parameters covered by the models. The low temperature inferred from evolutionary models indicates that HR 8799 b is ~400 K cooler than field L/T transition objects, providing further evidence that the L/T transition is gravity-dependent. With an unusually dusty photosphere, an exceptionally low luminosity for its spectral type, and hints of extreme secondary physical parameters, HR 8799 b appears to be unlike any class of field brown dwarf currently known.