Various single elements form incommensurate crystal structures under pressure, where a zeolite-type “host” sublattice surrounds a “guest” sublattice comprising 1D chains of atoms. On “chain melting,” diffraction peaks from the guest sublattice vanish, while those from the host remain. Diffusion of the guest atoms is expected to be confined to the channels in the host sublattice, which suggests 1D melting. Here, we present atomistic simulations of potassium to investigate this phenomenon and demonstrate that the chain-melted phase has no long-ranged order either along or between the chains. This 3D disorder provides the extensive entropy necessary to make the chain melt a true thermodynamic phase of matter, yet with the unique property that diffusion remains confined to 1D only. Calculations necessitated the development of an interatomic forcefield using machine learning, which we show fully reproduces potassium’s phase diagram, including the chain-melted state and 14 known phase transitions.