High-quality GaN and AlN have been grown by gas-source molecular beam epitaxy (MBE) using ammonia as the nitrogen source. A growth rate as high as 1 mu/h, which is an order-of-magnitude higher than previously reported for the growth of GaN by molecular beam epitaxy, has been achieved. Strong reflection high-energy electron diffraction intensity oscillations have been observed during the growth, making in situ thickness monitor and control as thin as one monolayer possible. Undoped GaN with an electron density as low as 2 x 10(17) cm(-3) and Mg-doped p-type GaN with a room temperature hole density of 4 x 10(17) cm(-3) were obtained. Low-temperature photoluminescence of as-grown materials was dominated by band-edge emissions, indicative of high-quality materials which are promising for applications to blue light emitters and high-temperature electronic devices.