Efforts to synthesize, characterize, and recover novel polynitrogen energetic materials have driven attempts to subject high nitrogen content precursor materials (in particular, metal and nonmetal azides) to elevated pressures. Here we present a combined theoretical and experimental study of the high-pressure behavior of ammonium azide (NH4N3). Using density functional theory, we have considered the relative thermodynamic stability of the material with respect to two other crystal phases, namely, trans-tetrazene (TTZ), and also a novel hydronitrogen solid (HNS) of the form (NH)(4), that was recently predicted to become relatively stable under high pressure. Experimentally, we have measured the Raman spectra of NH4N3 up to 71 GPa at room temperature. Our calculations demonstrate that the HNS becomes stable only at pressures much higher (89.4 GPa) than previously predicted (36 GPa). Our Raman spectra are consistent with previous reports up to lower pressures and at higher pressures, while some additional subtle behavior is observed (e.g., mode splitting), there is again no evidence of a phase transition to either TTZ or the HNS.