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Using an ab initio evolutionary structural search, we predict two novel crystalline phases in the H-N-O ternary phase diagram at high pressure, namely, NOH4 and HNO3 (nitric acid). Our calculations show that the C2/m phase of NOH4 becomes stable at 71 GPa, while the P21/m phase of HNO3 stabilizes at 39 GPa. Both phases remain thermodynamically stable at least up to 150 GPa, the maximum pressure we considered. The C2/m phase of NOH4 contains two O-H layers and one dumbbell cluster layer, formed by two NH3 molecules linked by a N-N covalent bond. The P21/m phase of HNO3 contains a surprising quasiclover layer formed of H-N-O covalent bonds. Further calculations show that both phases are semiconducting, with band gaps of 6.0 and 2.6 eV for NOH4 and NHO3, respectively. Our calculations also confirm that the compound NOH5(NH3H2O) becomes unstable at pressures above 122 GPa, decomposing into NH3 and H2O.