Conducting organic materials, such as doped organic polymers1, molecular conductors2,3 and emerging coordination polymers4, underpin technologies ranging from displays to flexible electronics5. Realizing high electrical conductivity in traditionally insulating organic materials necessitates tuning their electronic structure through chemical doping6. Furthermore, even organic materials that are intrinsically conductive, such as single-component molecular conductors7,8, require crystallinity for metallic behaviour. However, conducting polymers are often amorphous to aid durability and processability9. Using molecular design to produce high conductivity in undoped amorphous materials would enable tunable and robust conductivity in many applications10, but there are no intrinsically conducting organic materials that maintain high conductivity when disordered. Here we report an amorphous coordination polymer, Ni tetrathiafulvalene tetrathiolate, which displays markedly high electronic conductivity (up to 1,200 S cm-1) and intrinsic glassy-metallic behaviour. Theory shows that these properties are enabled by molecular overlap that is robust to structural perturbations. This unusual set of features results in high conductivity that is stable to humid air for weeks, pH 0-14 and temperatures up to 140 °C. These findings demonstrate that molecular design can enable metallic conductivity even in heavily disordered materials, raising fundamental questions about how metallic transport can exist without periodic structure and indicating exciting new applications for these materials.