Single photon emitters play a central role in many photonic quantum technologies. A promising class of single photon emitters consists of atomic color centers in wide-bandgap crystals, such as diamond silicon carbide and hexagonal boron nitride. However, it is currently not possible to grow these materials as sub-micron thick films on low-refractive index substrates, which is necessary for mature photonic integrated circuit technologies. Hence, there is great interest in identifying quantum emitters in technologically mature semiconductors that are compatible with suitable heteroepitaxies. Here, we demonstrate robust single photon emitters based on defects in gallium nitride (GaN), the most established and well understood semiconductor that can emit light over the entire visible spectrum. We show that the emitters have excellent photophysical properties including a brightness in excess of 500x10^3 counts/s. We further show that the emitters can be found in a variety of GaN wafers, thus offering reliable and scalable platform for further technological development. We propose a theoretical model to explain the origin of these emitters based on cubic inclusions in hexagonal gallium nitride. Our results constitute a feasible path to scalable, integrated on-chip quantum technologies based on GaN.