The ability of ceria to break H2 in the absence of noble metals has prompted a number of studies because of its potential applications in many technological fields. Most of the theoretical works reported in the literature are focused on the most stable (111) termination. However, recently, the possibility of stabilizing ceria particles with selected terminations has opened new avenues to explore. In the present paper, we investigate the role of termination in H2 dissociation on stoichiometric ceria. We model (111)-, (110)-, and (100)-terminated slabs together with the stepped (221) and (331) surfaces. Our results support a dissociation mechanism proceeding via the formation of a hydride/hydroxyl CeH/OH intermediate. Both the stability of such an intermediate and the activation energy depend critically on the termination, the (100)-terminated surfaces being the most reactive: the activation energy is 0.16 eV, and the CeH/OH intermediate is stable by -0.64 eV for the (100) slab, whereas the (111) slab presents 0.75 and 0.74 eV, respectively. We provide structural, energetic, electronic, and spectroscopic data, as well as chemical descriptors correlating structure, energy, and reactivity, to guide in the theoretical and experimental characterization of the Ce-H surface intermediate.