We idealise dendrite growth in a ceramic electrolyte by climb of a thick edge dislocation. Growth of the dendrite occurs at constant chemical potential of Li+ at the dendrite tip: the free-energy to fracture and wedge open the electrolyte is provided by the flux of Li+ from the electrolyte into the dendrite tip. This free-energy is dependent on the Li+ overpotential at the dendrite tip and is thereby related to the imposed charging current density. The predicted critical current density agrees with measurements for Li/LLZO/Li symmetric cells: the critical current density decreases with increasing initial length of the dendrite and with increasing electrode/electrolyte interfacial ionic resistance. The simulations also reveal that a void on the cathode/electrolyte interface locally enhances the Li+ overpotential and significantly reduces the critical current density for the initiation of dendrite growth.