We report the intercalation of iodine chains in highly crystalline arc-discharge multiwalled carbon nanotubes (MWCNTs), not in the central cavity but instead between the concentric graphene shells. High-resolution transmission electron microscopy demonstrated that the intercalation was asymmetric with respect to the longitudinal axis of the nanotubes. This filling is explained through the existence of asymmetric intershell channels which formed as the tubes shrank upon cooling after growth. Shrinkage occurred because the geometrically constrained equilibrium intershell spacing was higher at growth than room temperature, due to the highly anisotropic coefficient of thermal expansion of graphite (or graphene stacks). Computational modelling supported the formation of such cavities and explained why they all formed on the same side of the tubes. The graphene shells were forced to bend outward, thereby opening aligned intergraphene nanocavities, and subsequently allowing the intercalation with iodine once the tube ends were opened by oxidative treatment. These observations are specific to catalyst-free processes because catalytic processes use too low temperatures, but they are generally applicable in geometrically closed carbon structures grown at high temperatures and so should be present in all arc-grown MWCNTs. They are likely to explain multiple observations in the literature of asymmetric interlayer spacings in multiple-shell graphenic carbon structures.