Gas‐source molecular beam epitaxy (GSMBE), utilizing Ga and NH3, has been used to grow single‐crystal GaN(0001)1×1 on Al2O3(0001) substrates at temperatures Ts between 700 and 850 °C. In situ reflection high‐energy electron diffraction studies show a transition from three‐dimensional to two‐dimensional growth at Ts≳770 °C. For ≂1‐μm‐thick GaN layers, the best room‐temperature carrier mobilities, 100–110 cm2 V−1 s−1, with carrier concentrations of 1–4×1018 cm−3, were obtained at Ts≥780 °C. These are the highest reported mobilities for MBE GaN. Band‐to‐band photoluminescence was observed in these films at room temperature. Cross‐sectional transmission electron microscopy showed that the primary defects in the films were threading dislocations, with Burgers vectors a0/3〈2110〉, and stacking faults.