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 APM08279+5255 (z=3.91). Broad Paschen $alpha$ and $beta$ recombination lines of hydrogen were detected at wavelengths of 9.235 and 6.315microns, as well as a strong, red continuum that is a smooth power law over the observed (rest frame) wavelength range 5.3-35microns (1.08 - 7.1microns). The observed P$alpha$/P$beta$ line flux ratio of 1.05$pm$0.2 is far from the case B value of ~2 and simple models of high density, high optical depth ionized gas regions (~1.8). This deviation is opposite in sense to the expected effect of reddening. No evidence is found in the spectrum for either the 3.3micron or 6.2micron 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 APM08279+5255.