A number of exotic structures have been formed through high-pressure chemistry, but applications have been hindered by difficulties in recovering the high-pressure phase to ambient conditions (i.e., one atmosphere and 300 K). Here we use dispersion-corrected density functional theory [PBE-ulg (Perdew-Burke-Ernzerhof flavor of DFT with the universal low gradient correction for long range London dispersion)] to predict that above 60 gigapascal (GPa) the most stable form of N2O (the laughing gas in its molecular form) is a one-dimensional polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03∼0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions, both polymers relax below 14 GPa to the same stable nonplanar trans-polymer. The predicted phonon spectrum and dissociation kinetics validates the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a type of conducting nonlinear optical polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions (very high pressure or temperature).