ABSTRACT We use the time-independent quantum-mechanical formulation of reactive collisions in order to investigate the state-to-state H+ + HD → D+ + H2 chemical reaction. We compute cross-sections for collision energies up to 1.8 eV and rate coefficients for temperatures up to 10 000 K. We consider HD in the lowest vibrational level v = 0 and rotational levels j = 0–6, and H2 in vibrational levels v′ = 0–3 and rotational levels j′ = 0–9. For temperatures below 4000 K, the rate coefficients strongly vary with the initial rotational level j, depending on whether the reaction is endothermic (j ≤ 2) or exothermic (j ≥ 3). The reaction is also found less and less probable as the final vibrational quantum number v′ increases. Our results illustrate the importance of studying state-to-state reactions, in the context of the chemistry of the primordial universe.