Abstract: Provided are a method of producing single crystal AlN, single crystal AlN, and a single crystal AlN production apparatus with which single crystal AlN can be cheaply and continuously produced. The method of producing single crystal AlN includes a melt formation step of heating and melting an alloy to form a melt of the alloy and a deposition step of cooling a portion of the melt and providing a temperature gradient in the melt while causing deposition of single crystal AlN. In the deposition step, a nitrogen-containing gas is brought into contact with a high-temperature portion of the melt and a single crystal AlN seed crystal or a substrate for crystal growth is held in a low-temperature portion of the melt so as to continue to take nitrogen into the melt in the high-temperature portion while causing deposition of single crystal AlN.