We construct global multiple-coupled potential-energy surfaces for the three-dimensional Cl( ² P) + HCl → ClH + Cl( ² P) reaction which we use to generate results from quantum reactive scattering calculations. The three potential surfaces (1 ² A′, 2 ² A′ and 1 ² A″) are derived from multi-configuration self-consistent field (MCSCF) electronic structure calculations for geometries where all atoms are strongly interacting. The MCSCF energies are used to construct diabatic potentials which are fitted with rotated Morse cubic spline functions. The diabatic surfaces are then combined with empirical long-range potentials due to Dubernet and Hutson, which are also used to determine empirical coupling surfaces. Spin–orbit interaction is added perturbatively to the resulting surfaces. Saddle-point properties on these fitted surfaces are scaled to reproduce experimental thermal rate coefficient data based on the quantum scattering calculations. The quantum scattering calculations are based on a coupled-channel hyperspherical coordinate (CCH) method. The basis expansion used in the scattering calculation contains diatomic vibration and rotation, and the atomic fine-structure states, including full angular momentum coupling of rotation with electronic spin and orbital angular momentum. All terms in the combined rovibronic Hamiltonian are evaluated explicitly, including spin–orbit coupling, Coriolis and electrostatic interactions. State-selected and total cumulative reaction probabilities and thermal rate coefficients are calculated using a J-shifting approximation, which starts from converged CCH results for total angular momentum quantum number J = 1/2. The calculated rate coefficients indicate that spin-state change collisions account for a few per cent of the thermal rate coefficient at 300 K. Transition-state ClHCl resonances are lower in energy and broader than those on earlier (single) surfaces, and there is a more extensive progression in the symmetric stretch mode.