Using the NICMOS instrument on the Hubble Space Telescope, we have measured the dayside spectrum of HD 209458b between 1.5--2.5 microns. The emergent spectrum is dominated by features due to the presence of methane (CH4) and water vapor (H2O), with smaller contributions from carbon dioxide (CO2). Combining this near-infrared spectrum with existing mid-infrared measurements shows the existence of a temperature inversion and confirms the interpretation of previous photometry measurements. We find a family of plausible solutions for the molecular abundance and detailed temperature profile. Observationally resolving the ambiguity between abundance and temperature requires either (1) improved wavelength coverage or spectral resolution of the dayside emission spectrum, or (2) a transmission spectrum where abundance determinations are less sensitive to the temperature structure.