The Infrared Spectrograph ( IRS ) onboard the Spitzer Space Telescope ( SST ) has been used to obtain low and moderate resolution spectra of the dust and gas-rich quasar APM 08279+5255 ( z=3.91 ) . Broad Paschen \alpha and \beta recombination lines of hydrogen were detected at wavelengths of 9.235 and 6.315 \mu m , as well as a strong , red continuum that is a smooth power law over the observed ( rest frame ) wavelength range 5.3-35 \mu m ( 1.08 - 7.1 \mu m ) . The observed P \alpha /P \beta line flux ratio of 1.05 \pm 0.2 is far from the case B value of \sim 2 and simple models of high density , high optical depth ionized gas regions ( \sim 1.8 ) . This deviation is opposite in sense to the expected effect of reddening . No evidence is found in the spectrum for either the 3.3 \mu m or 6.2 \mu m emission features usually attributed to aromatic hydrocarbons in gas rich galaxies in the local Universe . This is consistent with the high luminosity AGN nature of APM 08279+5255 .