© 2020 Lithium-ion batteries with single ion-conductor ceramic electrolytes short-circuit when subjected to charging currents above a critical current density. Here, we analyse the rate at which a lithium (Li) filament (sometimes referred to as a dendrite) will grow from the cathode towards the anode during charging of such batteries. The filament is modelled as a climbing edge dislocation with its growth occurring by Li+ flux from the electrolyte into the filament tip at constant chemical potential. The growth rate is set by a balance between the reduction of free-energy at the filament tip and energy dissipation associated with the resistance to the flux of Li+ through the filament tip. For charging currents above the critical current density, the filament growth rate increases with decreasing filament tip resistance. Imperfections, such as voids in the Li cathode along the electrolyte/cathode interface, decrease the critical current density but filament growth rates are also lower in these cases as filament growth rates scale with the charging currents. The predictions of the model are in excellent quantitative agreement with measurements and confirm that above the critical current density a filament can traverse the electrolyte in minutes or less. This suggests that initiation of filament growth is the critical step to prevent short-circuiting of the battery.