For the first time, the equilibrium composition of chemical dissociation–recombination reaction is simulated from first-principles, only. Furthermore, beyond the conventional ab initio Born–Oppenheimer quantum chemistry the effects from the thermal and quantum equilibrium dynamics of nuclei are consistently included, as well as, the nonadiabatic coupling between the electrons and the nuclei. This has been accomplished by the path integral Monte Carlo simulations for full NVT quantum statistics of the \documentclass[12pt]{minimal}\begin{document}${\rm H}_3^+$\end{document}H3+ ion. The molecular total energy, partition function, free energy, entropy, and heat capacity are evaluated in a large temperature range: from below room temperature to temperatures relevant for planetary atmospheric physics. Temperature and density dependent reaction balance of the molecular ion and its fragments above 4000 K is presented, and also the density dependence of thermal ionization above 10 000 K is demonstrated.