The synthesis of large single crystals of GaN (gallium nitride) is a matter of great importance in optoelectronic devices for blue-light-emitting diodes and lasers. Although high-quality bulk single crystals of GaN suitable for substrates are desired, the standard method of cooling its stoichiometric melt has been unsuccessful for GaN because it decomposes into Ga and N-2 at high temperatures before its melting point. Here we report that applying high pressure completely prevents the decomposition and allows the stoichiometric melting of GaN. At pressures above 6.0 GPa, congruent melting of GaN occurred at about 2,220degreesC, and decreasing the temperature allowed the GaN melt to crystallize to the original structure, which was confirmed by in situ X-ray diffraction. Single crystals of GaN were formed by cooling the melt slowly under high pressures and were recovered at ambient conditions.