Single crystalline Li6.4Ga0.2La3Zr2O12 garnets were synthesized out of a melt using the Czochralski method. This method was chosen as it yields in large crystals with homogeneous elemental distribution compared to polycrystalline samples. For the synthesis, stoichiometric amounts of Li2CO3 (Alfa Aesar, 99.999%), La2O3 (Fox Chemicals, 99.999%) and ZrO2 ((Merck, Optipur) and Ga2O3 (Fox Chemicals, 99.999%) were mixed. Due to Li evaporation during the sintering step, an excess of 10 % Li2CO3 was added. For the preparation of the single crystals, the as-prepared polycrystalline LLZO samples were inductively heated and melted in an Ir crucible under N2 atmosphere. After supercooling the melt, an Ir wire was dipped into the crucible to induce crystal growth. This wire was then pulled out of the melt with a constant rate of 0.4 mm h -1 for 15 h with a rotation of 10 rpm until the melt was cooled down to room temperature. This resulted in a yellowish single crystal which was transparent in the inside and had a size of approximately Ø = 14 mm and h = 50 mm. For further experiments, the crystal was cut into pieces.