In this work, atomic layer etching (ALE) of thin film Ga-polar GaN(0001) is reported in detail using sequential surface modification by Cl2 adsorption and removal of the modified surface layer by low energy Ar plasma exposure in a standard reactive ion etching system. The feasibility and reproducibility of the process are demonstrated by patterning GaN(0001) films by the ALE process using photoresist as an etch mask. The demonstrated ALE is deemed to be useful for the fabrication of nanoscale structures and high electron mobility transistors and expected to be adoptable for ALE of other materials